(a) (i) Use Trapezoidal Approximation to estimate mum error of 10-³. -3x 3e dx with a maxi- 1 -3x (ii) Find the exact value of ² - dx and approximate the absolute error.

Q: x² dx %3D Use right endpoints and = 10 rectangles to find an approximation of

A: Given, Use the endpoints and n= 10 rectangles

Q: Let S be a linear transformation from R³ to R² with associated matrix Let T be a linear…

A: Let  be a linear transformation from  to  with associated matrix .Let  be a linear transformation…

Q: Suppose A is a 2 by 3 matrix. Does Ax = 0 always have infinitely many solutions? Give a reason. Does…

A:

Q: 4. C(x-xxx

A: 4. ∫-342x5-3x4+4x3dx Note:    Multiple questions are given, we are answer only one question. If you…

Q: (a) Integrate the following: 6. (i) (2Vx- 4) dx 1 (ii) 7-5x

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 1 x")dx

A: Use the following integration formulas: 1 ) Sum rule of integration 2 ) power rule of integration

Q: rnational event. However, the manager     lost his notes with accurate information on the number of…

A: Here, in the question, the manager of the non-profit company received the task by his boss to plan…

Q: 1. (2x + 1)(x - 5) dx

A:

Q: ~3 1 (c) dx (x 1) 3. -

A: Given query is to find the integral.

Q: 2. determine ∫12/5-2x dx by using substitution technique.

A: ∫125-2xdx  This is the integral given to us.we need to perform valid substitutions to evaluate the…

Q: d cosh(3x? + 1) and (b) dx d (sinh x tanh x). dx Calculate (a)

A: Given: a ddxcosh3x2+1b ddxsinhx tanhx

Q: Use the variation of parameters to solve the following equation: d^2y/dx^2- 3 (dy/dx)+2y=cos⁡(e^-x)

A: I am attaching image so that you understand each and every step.

Q: Evaluate. 9- xp- dx%3D Evaluate. dx | dx = Evaluate. dx dx =

A: As per guideline we have to solve 1st 3 parts

Q: = cos(x + y), when x = 0, y = " %3D

A:

Q: sin 5 (17x) dx = [

A: To evaluate : ∫sin517xdx Let I = ∫sin517xdx ⇒I =∫sin417xsin(17x) dx

Q: sinh e/2 dx is equal to e/2 2 cosh e 7/2 + C 2 cosh e"/2 + C O - (sinh e /2) + C 1 O -2 cosh e I/2 +…

A:

Q: Integrate 1. S the following: (x²-3x²) dx (x4-4x3+2)3 3 √x-2 z² 2 2. S dx 3. S dz 4 √73-2 3.

A:

Q: Find d/dx (arcsin (π/x^2))

A:

Q: Differentiate f(r)= (3x² + 10 – sin r)º. -

A: Given:- f(x) =(3x2+10-sin(x))  To find:- Derivative of f(x)

Q: 9. у %3D 4sin' (2xх) 10.у %3D tan? (x3) 11.у %3D sec(-х2 + 3х — 4)3

A: Question 9,Given,          y=4sin32x

Q: (9) 3 ov 1-1) dx

A:

Q: how do I implicitly differentiate, (solve for ds/dt) where: sqrt(t+s) = 2s

A: firstly, we square the both sides.

Q: Find the given derivative 6 Dx 7x 1 Dx 7x 5 LN +

A:

Q: m) -dx 1+sin(2x)

A:

Q: Solve S 1 (4x² - 9) ³/2 dx using trig sub and solve

A:

Q: j dx (2x-3) 15-12x+cx 2

A: As per the guidelines, we can be answered only for first question. Please repost the rest question…

Q: L' The Midpoint Rule approximation for -3x - 5x²) dx with n = = 3 is:

A:

Q: Use Trigonometric Substitutions dx 1. xVx +16 x*dx (x² – 1)"2 2. 3/2

A:

Q: Q4) Find for the following functions (- dx Зх +4 %3D 2x+3 6. y = tan-1 V4x3 - 3 %3D

A:

Q: The functions g(b, c, d) and h(b, c, d) are defined as: g = (b+ c+ d')' + (b' + c' + d') · (b' . c'…

A:

Q: (17) r/4- x² dx

A: