Question 2 Given that e' = e is the mathematical constant, calculate the integrals below using the following function: 1 f(x) = , where 1

Q: y = (sin x)e¯* find de sin-1y %3D d In x

A: y=sinxe-x. Then we have to find desin-1ydlnx.

Q: 1. dx nx e

A: Let I=∫1x(ln x)2dx

Q: ds 4. Evaluate s = In cot 20 in terms of de

A:

Q: 1 s vä (x + dx X

A:

Q: Calculate M6 for f(x) = 3 · ln(x²) over [1,2]. M6 = ←

A:

Q: Use implicit differentiation to find and 3yz? – x In(yz) = z. - dx dy

A: topic -  implicit differentiation

Q: d/S Vx5 dx el S- dx, (x # 0) 2x

A:

Q: 16. 0"(t)(t) = t sint

A: The objective of this question is to find the derivative of the function f(t) = t * sin(t).

Q: 7. 1 x lnx dx 8. f(x + 1)(2x - 1) dx

A: 7.∫1x lnxdx = ∫1 lnx. 1xdxLet, lnx= y ⇒1xdx = dySubstitute the corresponding values in the…

Q: 1. Kgothatso showed her classmates that dx%3D (x- 1) Without showing Kgothatso how you would…

A: 1.AgreeGiven Integral can be evaluated with the formula :∫yndy =yn+1n+1here y =x-1 , n=-23

Q: 3. If f(x) X-x find F(tanx) 1+x2

A: 7.The given limit is: limx→-∞x23x2-4x+1 To evaluate the value of the limit.

Q: Given that f(x) = x1°h(x) h( – 1) = 3 h'( – 1) = 6 - %3D Calculate f'( - 1).

A:

Q: Calculate M6 for f(x) = 7 · ln(x²) over [1,2]. M6 =

A:

Q: Use the table below to find y[5x + 4g(x)] dx x= 2 1 3. 4 f'(x) g'(x) 3 4 4 1 3. d. dx 5x+ 4g(x)]|…

A: We have ddx5x+4gx= 5ddxx+4dgxdx=5+4g'(x)

Q: Find dx 1 (a) COS (b) (c) when y = sin(loga (bx + c)), where a, b, and c are constants. b In a (bx +…

A:

Q: dx x (In² x – 6 In x + 10) -

A: The Answer is:      Result = arctan ( ln x - 3 ) + C

Q: find dy y = ln (1 + x2)

A: The given function is y=ln1+x2. Obtain the differential as follows.

Q: Let f ( x ) = ln ⁡ ( csc ⁡ x − cot ⁡ x ). Enter the value of f ′ ( π / 2 ).

A:

Q: Find dy using logarithnic dufferentiation dx Sinx Cosx tan?x 2-y=

A: Find dy/dx using logarithmic differentiation  Given y = x³√(1+x²)