Evaluate ft da 22-r-6 O a. 4ln r 3+ In r+2 +C O b. 4ln r+3- In a+2|+C c. 4ln a-3- In r+2 +C O d. 4ln a-3- In a-2|+C

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

A: This question is based on ratio test.

Q: Find the Taylor polynomials of orders n = 0, 1, 2, 3, and 4 about x = xo and then find the nth Taylo...

A: As we know that the nth order Taylor's polynomials at x=x0 is given by; pn=fx0+x-x011!f'x0+x-x022!f'...

Q: Write the factored form of the

A:

Q: Find the particular antiderivative that satisfies the following conditions: F' (x) = a* + 5Væ; F(1) ...

A:

Q: dy dr + y = x

A: We are asked to find the degree of the differential equation.

Q: Q6) Evaluate the following integral by using Odd and Even Powers Method: | cos* (;x) dx y =

A:

Q: k + 1 2(- 1)k+1 5k + 1 k=1 The series diverges. O The series converges.

A:

Q: Solve the initial value problem: (2x – 3y + 4)dx + (x – 1)dy = 0; y(-1) = 2. %3|

A:

Q: Find the derivative of the function without using the Quotient Rule. y 63 8(x)10

A:

Q: A plane flying horizontally at an altitude of 2 miles and a speed of 460 mi/h passes directly over a...

A: We can solve the given problem by using the Pythagorean theorem and the derivatives.

Q: a. When Frank initially sees the coyote, the angle of depression for his vision is 6 degrees. Draw a...

A: Frank stands at the top of a cliff. On the ground 310 feet below, frank spots a coyote.

Q: Consider the expression ſ V4 – x² dx = F(x)+C. The expression %3D F(2) – F(-2) is equal to

A: Here we have to evaluate F(2)-F(-2)=? We have, ∫4-x2dx=F(x)+C

Q: ollowing functions: b) y = (cos x)Vx*

A:

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

A:

Q: Determine whether the series converges; if so, find its sum. Otherwise type N in the blank. 1 k(k + ...

A: Given Series ∑k=1∞ 1kk+2  

Q: 12. Evaluate ((1– cos x) dx a.) 1- sin x +C b.)x - cos x +C c.) 1- cos x+C d.) x- sin x+C 13. Evalua...

A:

Q: Solve using the U-Technique Question 1 Consider the integral 2nx g(x) dx . There is a function g(x) ...

A: Given

Q: 1. S(z) = 64 –³ VI 2. -12r2 S(z) = 1+ 8x²

A:

Q: 1. If x - y = 25, then y" = c.) d.) - a.) b.) 2. If y = cos(3x+1), find y a.) 3 sin(3x+1) b.) -3 sin...

A: Authoring guideline: As per the authoring guidelines, we can solve only the first three parts. Repos...

Q: Solve the following differential equation xy = y(Iny- Inx) Select one: O a. In(2)- L: E CX O b. In(2...

A:

Q: Eliminate the parameter to find a Cartesian equation of the curve. 1 x(0) -cos 0 20 y(0) = 4 cos(20)...

A: (a)To determine: The cartesian equation by eliminating the parameter. (b) Range of x-values, express...

Q: Q2) Show that y = 35 x* – 30 x2 +3 satisfies ( 1- x² )y" – 2xy' + 20y = 0 %3D

A: y =35x4 - 30x2 +3 satisfy (1-x2)y" - 2xy' +20y =0 for this wew find  y" and y' y' = 140x3 - 60x y" =...

Q: (ke) 3 (1-In 2-) 1. For Sk*e3* dx = +C.f u= 3x, then k=? 2.

A:

Q: Use the ratio test for absolute convergence to determine whether the series converges or diverges. I...

A: In this question we have to find the value of the series and whether the series is converges of dive...

Q: Find the derivative of the function. f(z) = Vī – 8V7 f (x) 12r – 83x23

A:

Q: Find the derivative of the function. g(x) = 2(3 - 8x) g'(x)=

A:

Q: 2/Given frx)= 3Xtl a evaluate (flof(s) 1-SUEJECT NOTEBOOR 9. fo

A: Topic:-  function

Q: If g(x) f'(x) and if g(x) (cos x - x sin x)e*cosx, then f g(x) tan(f(x))dx is x cosx In(e*cosx) +€ s...

A:

Q: Car A is traveling west at 50 mi/h and car B is traveling north at 60 mi/h. Both are headed for the ...

A: topic - application of derivatives

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: Find the indefinite integral. (Use C for the constant of integration.) 9. dx XV 81 - (In x)2 |

A: Here we will solve the given integral,

Q: k If u = f (x), then f dx x4+2x2+1 +C for some constant k . Compute kf (1). x2+1 %3D

A: We have to find kf(1).

Q: If u = f(x), then S k dx = +C for some constant k. Compute kf(1). %3D x*+2x2+1 x2+1 4 -1

A: u=f(x)f(x)=xx2+2I=∫ xx4+2x2+1 dxI=∫ x dx(x2+1)2u=x2+1du = 2x dxx dx =du2

Q: Evaluate the integral. 7 sin-x dx +C NOTE: Enter the exact answer in expanded form.

A:

Q: k(k +7)

A:

Q: Evaluate the following integral. Sesim (5- In 2 dx 3

A:

Q: Find the Taylor polynomials of orders n = 0, 1, 2, 3, and 4 about x = xo and then find the nth Taylo...

A: To find the Taylor polynomials of orders n=0, 1, 2, 3, and 4 about x=x0 and then to find the nth Tay...

Q: Given: S 5x² cos 3x³dx. If u = 3x³, then the resulting integral is S f(u)du. Find f (*):- ... 5/7 5/...

A:

Q: Question 2 If S(16x4 – 16x³ + 4x²)dx = F(x) + C, then F(x) 16 A 5 4 x3+4x4 3 B (4x² – 2x) 3 16 4 x3 ...

A: The given integral is 16x4-16x3+4x2.

Q: Let s- dx be given . If u = e* + 1, then the resulting integral is S f(u) du. Compute f( er+1 3 A n ...

A: Given query is to find the value of f(3).

Q: 5. The standard form of the first order linear differential equation dy-(cscx-ycotx)dx=0is

A:

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

A: Here we have to find B*B*B. Where B ={x.y}

Q: Determine f(x) so that cos(In²x) f (x) dx = sin(In²x) + C

A: Let t =log2 x and follow step 2nd . 

Q: 6 for the Use sigma notation to write the Taylor series about x = function. 1 x+5 k =

A:

Q: Let u = 10TX. The differential of u with respect to x is du = 1072 20 7 Step 2 Rewrite the integrati...

A: topic - indefinite integral

Q: If g(x) = f'(x) and if g(x) = (cos x – x sin x)e* cos x, then S g(x) tan(f (x))dx is

A:

Q: an exponential function y f(x). (2,8.64) (1,7.2)

A:

Q: Each side of a square is increasing at a rate of 3 cm/s. At what rate (in cm²/s) is the area of the ...

A: We know that the area of the square is: A=b2 Where; b is the side of the square.   The Power law: d...

Q: II Simplify the following: 1. (ĀNBNČ) U (Ā nBN C)U (ĀNBNČ)U (ĀNB N C) U (A OBNČ)U (ANBN C) a. ĀU B b...

A: Distributive Property: (i) A∩BUC=A∩B∪A∩C(ii) A∪B∩C=A∪B∩A∪C Identity Law: (i) A∪A¯=U(ii)A∩U=A(iii)A¯∩...

Q: ssume that you are given the two matrices A and B below. If the multiplication matrix is qual to C, ...

A: