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Simple Calculus
Simple Calculus
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#math #forbeginners #self-evaluation #A-level #beginningcalculus
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Answers
1
∫ e
2x-1
dx
(1/2)ex + c
e2X-1 + c
2e2x-1 + c
(1/2)e2x-1 + c
2
f(x) = (2x
2
-3)/x ,from the eq. find the limit of f(x) approaching -1 .
-1
1
0
2
3
From equation: y = sin x ⋅ ln (2x) ,find y'. Tip: use power rule.
cos x ⋅ ln (2x) + sin x / 2
cos x ⋅ ln (2x) + sin x / x
sin x ⋅ ln x + sin x / x
cos x ⋅ sin x + ln (2x) / 2
4
f(x) = -9+6x-x
2
, find the root .
x = ± 3
x = 1/3
x = -3
x = 3
5
∫ (6x+2)/(3x
2
+2x) dx
ln (6x+2) + c
ln (1/3x2+2x) + c
ln (3x2+2) +c
ln (3x2+2x) + c
6
f(x) = 2x-1 ,fg(x) = (3x-4)/2 ,find g(x).
(2x-1)/2 + 1/4
(2x-1/4) + 1/2
(3x-4)/4 + 1/2
(3x-4)/2 + 1/2
7
Based on graph f(x) = (3x)
1/2
. Find the area from interval x=0 and x=6 . Tip: use integration.
2(216)1/2
2(72)1/2
2(72)1/3
-2(72)1/2
8
Who the well-knowed calculus inventor ?
Gottfried Leibniz
Leonardo Da Vinci
Albert Einstien
Isaac Newton
9
From eq. xy-x
2
-y=4 ,find the dy/dx implicitly.
(2x-y)/(x-1)
(x-y)/(x-2)
(y-2x)/(1-x)
(2x-y+4)/(x-1)
10
Which of the following is the
right
formula for derivatives by using by-part ?
uv' + ∫ v du
uv + ∫ v du
uv - ∫ v du
uv - ∫ u dv
