Calculate the Taylor polynomials T2(x) and T3(x) centered at a = 8 for f(x) = In(x +1). %3D

Q: nd two numbers whose sum is 24 with the condition that the sum of the square of one plus six es the ...

A: Topic:- calculus

Q: 1. Let E be the surface in R3 given by z = e-*-y where x2 + y² < 4, oriented with the upward normal....

A:

Q: This is a differential equations problem. Solve the following IVP's using the Laplace transform met...

A:

Q: Solve for a root/roots of the functions 2. x² – 3 sin x + 2 In(x + 1) = 3.5 Applying both a. Bisecti...

A: x2-3sinx+2ln(x+1)=3.5To Find: Roots of the function using bisection method and false position method...

Q: The derivative of the function y = cos(x ln 3)log3 (sin x) is:

A:

Q: Solve the following for dy/dx. Simplify fully. y = (9x?- 3)(4x + 3)2

A:

Q: Q.2\Prove the Maclaurin series: In(1+ x) = En=1' (-1)"-1x" ,-1<x< 1 . %3D

A: f(x) = ln(1+x)f0(0) = 0f1(x) =f'(x) =11+xf1(0) =1f2(x) =f''(x) =-1(1+x)2f2(0) =-1f3(x) =f'''(x) =2(1...

Q: i) State the change-of-base formula for logarithms. ii) Using the change-of-base formula, and the na...

A:

Q: 1. Find the y" of y (4x-3x + 1)9 (5x + 7)2 1/2

A:

Q: d.r r+5/+6

A:

Q: Find the radius of convergence and the interval of convergence. k(k + 4) Radius of convergence: Inte...

A:

Q: The derivative of the function y = tan-1 Vx2 – 1 + csc¬1 x, where x > 1 is: |

A:

Q: Find two points where the curve x^2+3xy+y^2=47 crosses the x-axis. The tangent lines to the curve at...

A:

Q: Find the area between the curves y = x2 - 8 and y = 4 - x.

A: Explanation of the answer is as follows

Q: Find the limits of the Follo CoS \im

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

Q: Question The derivative of the function y = cos(xln 3) log3(sin x) is:

A: We will find the derivative. 

Q: The Differentiation to be made must be based on the following topics. - Trigonometric Functions G...

A: recall: ddx(sinx)=cosxddx(xn)=nxn-1 Example 1: y=sin2x differentiating using chain rule dydx=ddx(sin...

Q: Find the domain of the function H(x)= 2x+3/33-4x

A: The domain of a function is the complete set of possible values of the independent variable

Q: 3. Find and and y= ivative of

A:

Q: inconclusive, then say so. 5* Σ 00 If p = + 0, enter "inty". i The series converges. The series dive...

A:

Q: Use the shell method to set up a definite integral (set up only, do not evaluate the integral) for t...

A:

Q: 1. Let E be the solid triangle in R³ whose corners are the points (1,0,0), (0, 1, 0) and (0,0, 2). C...

A: We have to compute the integral.

Q: Find b, given that LA = 500, 2C = 55º,a = 30. (Round to the nearest hundredth.) 55 b 30 50° A 37.8 2...

A:

Q: Find the longer diagonal of a parallelogram having sides of lengths 10 and 15 and an angle measure 6...

A:

Q: Compute the multiplicative inverses of the following (if they exist) usin Using the Euclidean algori...

A: Note: Since you have posted multiple questions we will solve the first question for you. If you want...

Q: Assume that the sequence shown below converges and find its limit. Võ, J8 + V5, 8+ /8+ võ 8+ /8+ /8+...

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: X+イ

A:

Q: Using the figure shown, find sing (3, - 4) -3/5 3/5 4/5 -4/5

A:

Q: 15 10 -6 -5 -4 -2 12 3 4 5 6 -5 10 -15 Determine the equation of the polynomial, f(2), of minimum de...

A:

Q: Find if the following is homothetic: F (x,y) = x²y +y3 %3D 1. Yes, it is homothetic. 2. No, it is no...

A: topic -  homogenous funtion

Q: Identify the problem whether a Permutation or Combination. Write the given of the problem and solve ...

A: Permutations and combinations

Q: r = 6(sec 0 + tan 0)3/2

A:

Q: Minimise x + y - 2xy subject to the constraint y 1: Answer:

A:

Q: The derivative of the function y = xe(5+sec(2x)) is: хе %3D

A: Explanation of the answer is as follows

Q: Q3) Evaluate the following integrals: sec(tan-1x). tan³ (tan-1 x) A) y = S dx 1+x2

A:

Q: The function f(x,y) = 2x + 2y has an absolute maximum value and absolute minimum value subject to th...

A: The given function is; f(x,y)=2x+2y and the given constraint is ; 9x2-9xy+9x2=16.

Q: 4. Find the equation for the line tangent to a. y=x²- 3 x + 5 at the point (2, 3)

A: We will find tangent equation. 

Q: For each of the following functions, determine: (a.) the critical numbers of f (b.) all relative ext...

A:

Q: A 3 X Y- X Y = 4xソーメニ2findr 3D2 and X"at X =1

A: Using definition of differentiation

Q: Use Green's Theorem to calculate ( - sen(a))da + (2a + 3)dy, where C is the triangle with vertices A...

A:

Q: 7. Given vectors ū =[2,1,4], v =[1,2,–1],and w=[x,1, z] find x and z such that ū x w = v.

A: u ×w = v now u × w = i    j    k                      2   1   4                      x   1   z now  ...

Q: Find y' for X= cos( sinx)

A:

Q: The roller coaster rides at Math Games are all shaped like trigonometric functions. Dan goes on the ...

A:

Q: 1. An inverted conical tank with 14 m height and 6 m radius at the top is full of water. Calculate t...

A:

Q: Q3) A) Graph the two equations and find the points in which graphs intersect x+y = 0, y= -(x- 1) TA ...

A: A) The graph is shown below:

Q: The graph of f(z) is given by {-1.4) (1, 4) (-1, –2) (5,-2) (3,-4) (-4, 5) Determine if f is continu...

A:

Q: Sy*ezdy

A:     ∫ y4ey2dyLet u=y2.=∫ 32euu4du=32·∫ euu4du=32u4eu-∫ 4u3eudu=32u4eu-4u3eu-3u2eu-2euu-euSubstitute ...

Q: Classify the series as absolutely convergent, conditionally convergent, or divergent. (-1)k+1 k7/6 k...

A: The given series is: ∑k=1∞(-1)k+1k76 Let, ak=(-1)k+1k76; k≥1

Q: Using appropriate substitution, the integral S ex3 dx is equal to: X4

A: Indefinite integral