dy d.x B) Does not exist If y = e- ln x then A) 0 when x = = 1 is O 210 18 D) 1/12 E) e

Q: 2. Which of the following functions is of exponential order? * 4 f(t)= Sin 4t f(t)= 5{VT + A.) O B.)…

A: The function of exponential order is determined as shown below.

Q: [r² dy a) Prove that, fo-y4= 4a√/2m

A: note :Since you have posted multiple questions, we will provide the solution only to the first…

Q: dy Calculate dx You need not expand your answer. E+2) x- O a. Ob. 1 Vx + 4x /x + x, Oc. x + 1 4 d.…

A: Product rule of derivative is : (d/dx)(f•g) (f • g) ' = f ' • g + f • g ' Here f ' = d f / d x and…

Q: da Evaluate x² V4

A:

Q: 1 d) ₁ √²-7 dx

A:

Q: Q5: Simplify the following then find the dy /dx a) y = (logy y2*) (estn 2*) (tan-!x)

A: Since you have asked multiple questions in single request,  So we will be answering only first…

Q: 1. Evaluate: a) S x³ sec-1(ln (x)) dx

A:

Q: Sketch and evaluate the reverse in tegral 9/x dy dz

A: Consider the provided integral,

Q: Let H„(x) = (-1)" -w that h, E L² (R). , x € R, n E No, and let h„(x) dan e H„(x)e¯

A: Given: Hnx=-1nex2dndxne-x2 x∈ℝ, n∈ℕ0 This is a Hermite polynomial function. hnx=Hnxe-x22 To…

Q: d e) (In|sin x)) dx

A:

Q: d Prove that (x") = n x"-1 dx

A:

Q: Show that S, (In x)? dx = e – 2

A: The detailed solution is as follows below:

Q: (1+x° 2) 늪(cot-1 () - d dx 1-x,

A: Solution:To find:ddx cot-1 1+x1-x=?Formula:ddxcot-1x=-11+x2ddxuv=vu'-uv'v2

Q: 3 a) Given fg(x)dx=5, [[3g(x)– 4h(x)]dx = 27 . i) Find [h(x)dx . ii) Hence, evaluate [4x – 3h(x)]dx.

A:

Q: d) Bessel function, Show that So Jo(x) dx = 1.

A:

Q: (ii) ſĩ 7(1+ln² t) 4 t(1+In² t)dt

A:

Q: For the function y = x² + 2x, the value of dy when *=3 and dx=0.1 js -0.15 A) 0.15 B) C) - 0.8 0.8…

A: We will find out the required value.

Q: Solve for x in the interval 0 < x < 2n. log (sin (x)) – log (cos (x)) = 0 a) x = 5,

A:

Q: By substitution, z=ln(x), the equation, x2y''+2y=0, will be transformed to an equation in the form…

A:

Q: If f(x) : = 4 In(x² + x + 1), at what value of X is f' (x) = 4? O a) -1 O b) 2 O c) o d) None of…

A: This question can be solved using the concept of differentiation of function of function.

Q: x In x dx

A: Since you have asked multiple questions in single request.so we will be answering only first…

Q: Prove that : L₁₁ (1-x²) PP dx = 0. 2n(n+1) 2n + 1 . mn. m1 = 11. m, ne N

A:

Q: S f(x)dx

A:

Q: = xp- 1+e* A e2x + In(1+ e*) + C ® e* – In(1+ e*) + C B © 2e2x - In(1 + e*) + C_ D e2x – In(1 + e*)…

A:

Q: If sinh(æ) = -4 , then coth(x) = (A) (B) =VI7 (C) =VE V15 (D) 4 15 (E) E O (A) O (B) o (c) O (D) O…

A: Solution

Q: 1. Find In(x²+1) X2 dx.

A: