Given the the parametric curve S2(t) = ¿e4 – l y(t) 12et + 32t 1 t5 – 6t + 10 dy (a) Find an expression for dy = dx (-) 23 1 (b) Find the slope of the tangent line at the point Find the exact value, no decimals. 2' 10 m (c) Find the value(s) of t where there is a horizontal tangent line. Find the exact value(s) of t, no decimals. t : (d) Find the value(s) of t where there is a vertical tangent line. Find the exact value(s) of t, no decimals. t =

Q: 2 tan(4x-1)-3 cos² (4x-1) If we let u = 4x – 1 for the dx, what will be the resulting integrand? cos...

A:

Q: 6. ху\ + (1+х)y %3Dе*, у(1) — 0 7. sinx y'+2y cosx = sin2x, y : 2 6.

A:

Q: Plot the following functions 2. y = (x – 1)3 + 2

A: Topic = Function

Q: Prove that the given equation is a solution to the given DE: 1. = C,e3* + C2e2x + C3e* ; y" – 6y" + ...

A: As you have asked for the solution of Question 3-5 only. So I am solving those only. Hope it helps y...

Q: Use the ratio test to determine whether the series converges. If the test is inconclusive, then say ...

A: This is a problem related to series calculation. Based on the ratio test we will determine the natur...

Q: Solve the following differential equation (1+x)y' – y=0 Select one: O a. Inlyl=In|1-2xl)+c O b. Inly...

A:

Q: Find the Maclaurin polynomials of orders n = 0, 1, 2, 3, and 4 and then find the nth Maclaurin polyn...

A: Please see the below picture for detailed solution. 

Q: For the following primitives, identify the number of essential constants.(x and y are the variables)...

A:

Q: Determine whether the series is convegent or divergent. If it is Convergent, find its sum. If s an=l...

A:

Q: Find the derivative of f(x) = sec(tan(x) + cot(x))

A:

Q: Determine Functions Directions: Determine which relations represent a function and then drag each in...

A:

Q: " + y = 12 cos 2x - sin x. A. " + y = sin 3x +4 cos x. A

A: Given: y''+y=12cos2x-sinx

Q: dx The integral S reduces to S k, where u = f(x) and for some constant k . Compute f(1). ex+1

A:

Q: Find the indefinite integral. (Use C for the constant of integration.) 4 cos(0) – 1 OP

A:

Q: Let A= [a, b c, d, e) and B=(a, b, c, d, e f g, h). Match the given sets in the left to the sets in ...

A:

Q: Which substitution is best to use in order to solve the integral / 2sinx cos xdx? Select one: u=cos ...

A:

Q: Determine the critical numbers of the ff. functions.

A:

Q: Find the derivative of y with respect to x for y = sinh 1(11/15x). dy 165 dx 2/1815x? + 15x

A: Given query is to find the derivative of the expression.

Q: 2:(y-x² )dx+ dy =0 1.

A:

Q: Solve the system. 3x + 6y - z = 7 2х - Зу + 5z %3D -11 8x + 9y – 2z = 13 The solution set is {010} (...

A:

Q: Problem 2: A piece of string whose length is given below is cut into two pieces. One piece is used t...

A:

Q: 3T en: S 5x² cos 3x³dx. If u = 3x³, then the resulting integral is S f(u)du. Find f (").

A: Given query is to find the indicated function.

Q: If cotx 12 find the other trigonometric functions

A: We will use the basic trigonometric formulae to solve this question.

Q: 3. a) Determine whether or not the point R(-3, 4, -2) lies on the line i = [0,20,4]+t[1,4,–2].

A: Given

Q: Question 13 Using u-substitution, the integral S f(x)dx reduces to a new integral ſ g(u)du. If g(u) ...

A: Here, given that: ∫f(x) dx=x+ln (x-1)+c...(1)

Q: Evaluate the integral. 5 x2 e dx +C

A:

Q: Solve the initial value problem. dy + 5xy = 8x, y(0) = - 6 dx y =

A: topic - differential equations

Q: (-4x-12) dx For J x+10)³ (x-4)³ F(x) – 1. What is F(3)? -

A: Given: ∫-4x-12x+103x-43dx=Fx-1   ...(1)  

Q: (1 - V2) dt 44. 46. (2z – 3) dz - 3

A:

Q: Question d²y Find if -9x – 3y = 8. %3D dx2

A: Detail solution is given below

Q: т?+2m Consider dm. If we let u = m + 1, what will be the resulting integral as a function of u? m+1

A:

Q: find the function y(x) satisfying dx/dy=5x ^(-6/7) and y(-1)=-2

A:

Q: 1+ In x Find f (x) so that when u = f(x) the integral dx can be rewritten as cot u du tan(f(x))

A: So our approach in this question by substitution method . We can assume a function u in terms of 'x'...

Q: x² + y? = r2 O y = - y' = - y

A: topic - differential equation

Q: Use the disk/washer method to set up a definite integral (set up only, do not evaluate the integral)...

A:

Q: Use the ratio test to determine whether the series converges or diverges. If the test is inconclusiv...

A: Given series  ∑k=1∞5kk!

Q: Find the interval of convergence of the power series. (Be sure to include a check for convergence at...

A:

Q: Required information NOTE: This is a multi-part question Once an answer is submitted, you will be un...

A:

Q: If §dx = A(B In|2 + x| + D In|2 – x) + C, then the value of 2A(B – D) is

A: This question can be solved by using the concept of some special integrals.

Q: 27. What is the simplest form of sin 2 tan'x A) 1+x B) 21+x? 2x C) 1+x 2x D) |1+x?

A:

Q: Solve the initial value problem: dy/dx= (5x^4)(y^4) ; y(0)= 1/2

A:

Q: Find the standard (slopc-intcrcept form) cquation of the tangent linc to the following functions at ...

A: find equation of tangent line please like if your problem resolve

Q: If the solution to ſe2* sec²(e²×+1)dx is equal to k tan(e2x+1) + C , find the exact value of k.

A: We know, ∫sec2(x)dx=tan(x) ddxemx=memx

Q: if 4x1

A: Given problem:-

Q: If cotx 12 find the other trigonometric functions

A: Given query is to find the values of trigonometric functions.

Q: 4 Find the sum of the series E (2n + n³) n =1

A:

Q: The integral / 2cos(2')dr takes the form & cosar du when =2 and/(x)=x-5 What is the value of (+2)? 2...

A:

Q: (9cosx+y°cosx) dx +2ysinx dy = 0, y(5)= -4 the value of the constant (c) of this D.E will be:

A: Solution is written in below steps.

Q: 1.J347x2+12x .s 3x2+8x-12 dx

A: 1). Given: I=∫3x2+8x-12x3+7x2+12xdx We know that; ∫1ax+bdx=1alnax+b+C   Note: As per Bartleby guidel...

Q: Write the equation of the sphere if (1, - 2, of the sphere. 5) and (- 1, - 2, - 7) are the end point...

A: Solving question by equation of sphere