DIFFERENTIATION OF TRIGOMETRY
(1). Differentiate y = x5 sin x
(A) x(x cos x + 5 sin x) (B) x2(x cos x + 5 sin x) (C) x4(x cos x + 5 sin x) (D) x5(x cos x + 5 sin x)
Solution:-Using CASIO fx-991MS calculator
--when performing differential equation involving trigometry using CASIO fx-991MS calculcator ensure that the angle is in radian mode. To impute it press
[ON] [MODE] [MODE] [MODE] [MODE] [2]
--ensure that your calculcator is in 2 significance figures to impute it press
[MODE] [MODE] [MODE] [MODE] [MODE] [2] [2]
Y = x5 sin x :. Make x = any number of choice i.e. x = 9 i.e. x = 9 =“[,] [9] [,]”
[AC] [SHIFT] [d/dx] [ALPHA] [X] [^] [5] [sin] [ALPHA] [X] [,] [9] [,] [1] [EXP] [-] [5] [)] [=] (-4.0 X 104) to 2 s.f
Checking any of the option (A), (B) (C), (D) the option gives -4.0 x 104 it is correct but if it didn’t give -4.0 x 104 it is wrong
Checking option (A) x(x cos x + 5 sin x)
[AC] [ALPHA] [X] [(] [ALPHA] [X] [COS] [ALPHA] [X] [+] [5] [SIN] [ALPHA] [X] [)] [=] (-5.5 X 101)
Option (A) is wrong
Checking option (B) x2(x cos x + 5 sin x)
[AC] [ALPHA] [X] [x2] [(] [ALPHA] [X] [COS] [ALPHA] [X] [+] [5] [SIN] [ALPHA] [X] [)] [=] (-5.0 X 104)
Option (B) is wrong
Checking option (C) x4(x cos x + 5 sin x)
[AC] [ALPHA] [X] [^] [4] [(] [ALPHA] [X] [COS] [ALPHA] [X] [+] [5] [SIN] [ALPHA] [X] [)] [=] (-4.0 X 104)
Option (C) is correct
Checking option (D) x5(x cos x + 5 sin x)
[AC] [ALPHA] [X] [^] [5] [(] [ALPHA] [X] [COS] [ALPHA] [X] [+] [5] [SIN] [ALPHA] [X] [)] [=] (-3.6 X 105)
Option (D) is wrong The correct option is option “C”
(2). Differentiate y = cos x/sin x
(A)–cosec2 x (B) cos2 x (C) tan2 x (D) sec2 x
Solution:-Using CASIO fx-991MS calculator
--when performing differential equation involving trigometry using CASIO fx-991MS calculator ensure that the angle is in radian mode. To impute it press
[ON] [MODE] [MODE] [MODE] [MODE] [2]
--ensure that your calculcator is in 2 significance figures to impute it press
[MODE] [MODE] [MODE] [MODE] [MODE] [2] [2]
Make x = 10 but x = 10 = [,] [1] [0] [,] ,, use key [1] [EXP] [-] [5] to solve any differential equation given
[ON] [SHIFT] [d/dx] [(] [cos] [ALPHA] [X] [)] [ab/c] [(] [sin] [ALPHA] [X] [)] [,] [9] [,] [1] [EXP] [-] [5] [)] [=] (-5.9 X 100)
Checking option (A), (B), (C), (D) If any of the option gives (-5.9 X 100) it is correct but if it did not give (-5.9 X 100) it is wrong
Checking option (A)-cosec2x
But cosec2x = 1/sin2 x = 1/(sin x)2
[AC] [(-)] [1] [ab/c] [(] [sin] [ALPHA] [X] [)] [x2] [=] (-5.9 X 100)
Option (A) is correct
Checking option (B) cos2 x
[AC] [(] [cos] [ALPHA] [X] [)] [x2] [=] (8.3 X 10-1)
Option (B) is wrong
Checking option (C) tan2 x
[AC] [(] [tan][ALPHA] [X] [)] [x2] [=] (2.0 X 10-1)
Option (C) is wrong
Checking option (D) sec2 x
sec2 x =1/cos2 x = 1/(cos x)2
[AC] [(-)] [1] [ab/c] [(] [cos] [ALPHA] [X] [)] [x2] [=] (1.2 X 100)
Option (D) is wrong The correct option is option “D”
(3). Differentiate y = tan x/ex
(A) Sec2x + tan x (B) sec2 x – tan x (C) tan x + sec x (D) sec x + tan2 x
ex ex ex ex
Solution :-Using CASIO fx-991MS calculator
[ON] [SHIFT] [d/dx] [(] [TAN] [ALPHA] [X] [)] [ab/c] [ALPHA] [ℓ] [^] [ALPHA] [X] [,] [9] [,] [1] [EXP] [-] [5] [)] [=] (2.0 X 10-4)
Checking option (A) Sec2x + tan x
ex
but sec2 x = 1/cos2 x = 1/(cos x)2 :. Sec2x + tan x = 1/(cos x)2 + tan x
ex
--when dividing the numerator and the denominator put brackets to avoid errors except it is a whole number i.e. “(1/(cos x)2 + tan x)
ex
[AC] [(] [1] [ab/c] [(] [cos] [ALPHA] [X] [)] [x2] [+] [tan] [ALPHA] [X] [)] [ab/c] [ALPHA] [ℓ] [^] [ALPHA] [X] [=] (9.3 X 10-5)
Option (A) is wrong
Checking option (B) sec2 x – tan x
ex
but sec2 x = 1/cos2 x = 1/(cos x)2
[AC] [(] [1] [ab/c] [(] [cos] [ALPHA] [X] [)] [x2] [-] [tan] [ALPHA] [X] [)] [ab/c] [ALPHA] [ℓ] [^] [ALPHA] [X] [=] (2.0 X 10-4)
Option (B) is correct
Checking option (C) tan x + sec2 x
ex
but sec2 x = 1/cos2 x = 1/(cos x)
[AC] [(] [ tan] [ALPHA] [X] [+] [cos] [ALPHA] [X] [)] [ab/c] [ALPHA] [ℓ] [^] [ALPHA] [X] [=] (-1.9 X 10-4)
Option (C) is wrong
Checking option (D) sec x + tan2 x
ex
but sec2 x =1/cos2 x = 1/(cos x)2
[AC] [(] [1] [ab/c] [cos] [ALPHA] [X] [+] [(] [tan] [ALPHA] [X] [)] [x2] [)] [ab/c] [ALPHA] [ℓ] [^] [ALPHA] [X] [=] (-1.1 X 10-4)
Option (D) is wrong
(1). Differentiate y = x5 sin x
(A) x(x cos x + 5 sin x) (B) x2(x cos x + 5 sin x) (C) x4(x cos x + 5 sin x) (D) x5(x cos x + 5 sin x)
Solution:-Using CASIO fx-991MS calculator
--when performing differential equation involving trigometry using CASIO fx-991MS calculcator ensure that the angle is in radian mode. To impute it press
[ON] [MODE] [MODE] [MODE] [MODE] [2]
--ensure that your calculcator is in 2 significance figures to impute it press
[MODE] [MODE] [MODE] [MODE] [MODE] [2] [2]
Y = x5 sin x :. Make x = any number of choice i.e. x = 9 i.e. x = 9 =“[,] [9] [,]”
[AC] [SHIFT] [d/dx] [ALPHA] [X] [^] [5] [sin] [ALPHA] [X] [,] [9] [,] [1] [EXP] [-] [5] [)] [=] (-4.0 X 104) to 2 s.f
Checking any of the option (A), (B) (C), (D) the option gives -4.0 x 104 it is correct but if it didn’t give -4.0 x 104 it is wrong
Checking option (A) x(x cos x + 5 sin x)
[AC] [ALPHA] [X] [(] [ALPHA] [X] [COS] [ALPHA] [X] [+] [5] [SIN] [ALPHA] [X] [)] [=] (-5.5 X 101)
Option (A) is wrong
Checking option (B) x2(x cos x + 5 sin x)
[AC] [ALPHA] [X] [x2] [(] [ALPHA] [X] [COS] [ALPHA] [X] [+] [5] [SIN] [ALPHA] [X] [)] [=] (-5.0 X 104)
Option (B) is wrong
Checking option (C) x4(x cos x + 5 sin x)
[AC] [ALPHA] [X] [^] [4] [(] [ALPHA] [X] [COS] [ALPHA] [X] [+] [5] [SIN] [ALPHA] [X] [)] [=] (-4.0 X 104)
Option (C) is correct
Checking option (D) x5(x cos x + 5 sin x)
[AC] [ALPHA] [X] [^] [5] [(] [ALPHA] [X] [COS] [ALPHA] [X] [+] [5] [SIN] [ALPHA] [X] [)] [=] (-3.6 X 105)
Option (D) is wrong The correct option is option “C”
(2). Differentiate y = cos x/sin x
(A)–cosec2 x (B) cos2 x (C) tan2 x (D) sec2 x
Solution:-Using CASIO fx-991MS calculator
--when performing differential equation involving trigometry using CASIO fx-991MS calculator ensure that the angle is in radian mode. To impute it press
[ON] [MODE] [MODE] [MODE] [MODE] [2]
--ensure that your calculcator is in 2 significance figures to impute it press
[MODE] [MODE] [MODE] [MODE] [MODE] [2] [2]
Make x = 10 but x = 10 = [,] [1] [0] [,] ,, use key [1] [EXP] [-] [5] to solve any differential equation given
[ON] [SHIFT] [d/dx] [(] [cos] [ALPHA] [X] [)] [ab/c] [(] [sin] [ALPHA] [X] [)] [,] [9] [,] [1] [EXP] [-] [5] [)] [=] (-5.9 X 100)
Checking option (A), (B), (C), (D) If any of the option gives (-5.9 X 100) it is correct but if it did not give (-5.9 X 100) it is wrong
Checking option (A)-cosec2x
But cosec2x = 1/sin2 x = 1/(sin x)2
[AC] [(-)] [1] [ab/c] [(] [sin] [ALPHA] [X] [)] [x2] [=] (-5.9 X 100)
Option (A) is correct
Checking option (B) cos2 x
[AC] [(] [cos] [ALPHA] [X] [)] [x2] [=] (8.3 X 10-1)
Option (B) is wrong
Checking option (C) tan2 x
[AC] [(] [tan][ALPHA] [X] [)] [x2] [=] (2.0 X 10-1)
Option (C) is wrong
Checking option (D) sec2 x
sec2 x =1/cos2 x = 1/(cos x)2
[AC] [(-)] [1] [ab/c] [(] [cos] [ALPHA] [X] [)] [x2] [=] (1.2 X 100)
Option (D) is wrong The correct option is option “D”
(3). Differentiate y = tan x/ex
(A) Sec2x + tan x (B) sec2 x – tan x (C) tan x + sec x (D) sec x + tan2 x
ex ex ex ex
Solution :-Using CASIO fx-991MS calculator
[ON] [SHIFT] [d/dx] [(] [TAN] [ALPHA] [X] [)] [ab/c] [ALPHA] [ℓ] [^] [ALPHA] [X] [,] [9] [,] [1] [EXP] [-] [5] [)] [=] (2.0 X 10-4)
Checking option (A) Sec2x + tan x
ex
but sec2 x = 1/cos2 x = 1/(cos x)2 :. Sec2x + tan x = 1/(cos x)2 + tan x
ex
--when dividing the numerator and the denominator put brackets to avoid errors except it is a whole number i.e. “(1/(cos x)2 + tan x)
ex
[AC] [(] [1] [ab/c] [(] [cos] [ALPHA] [X] [)] [x2] [+] [tan] [ALPHA] [X] [)] [ab/c] [ALPHA] [ℓ] [^] [ALPHA] [X] [=] (9.3 X 10-5)
Option (A) is wrong
Checking option (B) sec2 x – tan x
ex
but sec2 x = 1/cos2 x = 1/(cos x)2
[AC] [(] [1] [ab/c] [(] [cos] [ALPHA] [X] [)] [x2] [-] [tan] [ALPHA] [X] [)] [ab/c] [ALPHA] [ℓ] [^] [ALPHA] [X] [=] (2.0 X 10-4)
Option (B) is correct
Checking option (C) tan x + sec2 x
ex
but sec2 x = 1/cos2 x = 1/(cos x)
[AC] [(] [ tan] [ALPHA] [X] [+] [cos] [ALPHA] [X] [)] [ab/c] [ALPHA] [ℓ] [^] [ALPHA] [X] [=] (-1.9 X 10-4)
Option (C) is wrong
Checking option (D) sec x + tan2 x
ex
but sec2 x =1/cos2 x = 1/(cos x)2
[AC] [(] [1] [ab/c] [cos] [ALPHA] [X] [+] [(] [tan] [ALPHA] [X] [)] [x2] [)] [ab/c] [ALPHA] [ℓ] [^] [ALPHA] [X] [=] (-1.1 X 10-4)
Option (D) is wrong
Unforgiveness is a sin, if you don’t forgive; your trespasses (sins) will not be forgiven
Reason. In Mathew 6:14-15- if
ye forgive men their trespasses your heavenly father will also forgive
your trespasses but if ye forgive not men their trespasses neither will
your father forgive your trespasses
Also in Mark 11:25-26- And
when ye stand praying forgive if you have ought against any that your
father also which is in heaven will forgive your trespasses. But if ye
do not forgive, neither will your father which is in heaven forgive your
trespasses.
For
your heavenly father to forgive your trespasses. You must forgive those
that trespass against you including your enemies. In Matthew 5:44-Love
your enemies, bless them that curse you, do good to them that hate you,
pray for them which despitefully use you and persecute you. As a
Christian/Believer of JESUS CHRIST you must forgive your enemies
including those that commit evil against you because if you don’t
forgive them you are in darkness. In 1 John 2:9-11 – He that
saith he is in the light and hateth his brother is in darkness even
until now. He that loveth his brother abideth in the light and there is
none occasion of stumbling in him. But he that hateth his brother is in
darkness and walketh in darkness and knoweth not wither because that
darkness has blinded his eyes. A believer will say I am in the light
by being a deacon, choir, usher, pastor, evangelist, But know that
Christians/believers who is indulge in unforgiveness will not inherit
the kingdom of God and they will spend their eternity in hell (the fire
that never shall be quenched). Mark 9:43
Know
that if you don’t forgive today, your prayers will not be answered. But
if you are touched by the word of GOD on unforgiveness and you have
make a decision in your heart to forgive whomsoever wronged you, offend
you, please make this confession
LORD
JESUS, as I come to you, have mercy upon me, as I forgive those that
offend me today. Forgive me my trespasses; receive me into your kingdom,
IN JESUS NAME AMEN.
NOW: that you have confess this prayer of unforgiveness you are free to confess the next prayer below if you are not
Born-again
if
you have not born-again or given your life to Jesus Christ say this
prayer “Lord JESUS, as I come to you today, Have mercy upon me, Forgive
me all my sins, wash me with your precious blood, save my soul, as I
receive you today as my lord and personal savior, write my name in the
book of life, IN JESUS NAME AMEN.
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