Find f(x) and g(x) such that h(x) = (f o g)(x). Let g(x) = 2x + 1. 3 h(x) = /2x+1 f(x) =|

Q: Find the Taylor series generated by fat x = a. f(x) = 9*, a = 3 Choose the correct answer below. 729...

A:

Q: Find the eguation of the tangent Line to the CUrre y= Cos( Son)e) at the Point mith coordinates (T) ...

A: This question is related to application of derivatives.

Q: x-4 Evaluate the integral x²-5x+6 = (x-2)(x-3) х2-5х+6

A:

Q: A trough is 16 ft long and its ends have the shape of isosceles triangles that are 3 ft across at th...

A: A trough is 16 ft long and its ends have the shape of isosceles triangles that are 3 ft across at th...

Q: Critique the validity of the expression d2y dy dx2 dx A) It is not valid, because the notation d?y d...

A: The objective is to critique the validity of the expression. 

Q: Without using a calculator, find the exact value of each: i. sin-1(sin)) =

A: topic- inverse trigonometric functions sin(π+θ)=-sin(θ)sin-1(-x)=-sin-1(x)

Q: Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant ) ...

A:

Q: Represent the function 8ln(8−x) as a power series (Maclaurin series) What is the radius of converge...

A: Given:- The function is, f(x)=8ln(8-x) as a power series. To find: - The radius of convergence of th...

Q: Discuss the similarities and differences between what it means for a sequence to converge and what i...

A: Sequence and series. 

Q: Find the derivative of the function. y = a6 + cos6 x y'(x) =

A: Given

Q: 13 Find the Maclaurin series for f(x) = 1+x 13 -? 1+x What is the Maclaurin series of

A:

Q: Use the Arc Length Theorem to calculate the length s of the path over the interval. (sin(0) – 0 cos(...

A: Given : (sinθ - θcosθ, cosθ + θsinθ);            0 ≤ θ ≤9

Q: Consider the initial value problem y'(t) = Y(0) = 3. 2y a. Use Euler's method with At = 0.1 to compu...

A: The given initial value problem is: y'(t)=12y ;         y(0)=3Here f(t,y)=12y,    t0=0,  y0=3

Q: Find f(3,4) for f (x, y) = In(x + /x² + y²). %3D

A: Given:- f(x, y) =ln(x+√(x2+y2))  To find:- fx(x, y) at (3, 4) 

Q: 3. Complete the table for the function: y 21 Xy a 0 b 4 C 6 a= b= 2.

A: Topic = Function a=2 b=4 c=5

Q: Let g(x, y) = cos(x + 2y). a. Evaluate g(2,–1). b. Find the domain of g. c. Find the range of g.

A: The function,      g(x,y)=cosx+2y

Q: Find the Taylor polynomial of orders 0, 1, 2, and 3 generated by f at a. 5x f(x) = cos x, a = 6 Po(x...

A:

Q: Solve the limit:

A:

Q: Find a simplified form of the difference quotient for the function. 8 f(x) = x2

A: We have to find simplify form

Q: Write the equation of a sine function that has the given characteristics. The graph of y = x, shifte...

A: Given a function f(x),a new function g(x)=f(x)+k,where k is a constant, is a vertical shift of the f...

Q: Find a simplified form of the difference quotient for the function. f(x) = /x- 8

A: Difference quotient for function f(x)=x-8

Q: ii. cos(cos-G

A: Given query is to perform indicated trigonometric operation.

Q: Find the differential of each f (a) y = 1 + 4s dy =

A: Since you have asked multiple question, we will solve the first question for you as per our guide li...

Q: a/2 2. Evaluate f[(e)i-2sin(t) j+3cos(1)k]dt

A:

Q: 7. Find T, N, ar, an at t=n. r(1) = 4cos(1)i–4sin(r)j-3rk

A: Tt = r'(t)r'(t) and N(t) = T'(t)T'(t) aT = r'(t) .r''(t)r'(t) and aN = r'(t)×r''(t)r'(t)

Q: Find equations of the tangent plane and normal line to the surface z + 19 = xe cos z at the point (1...

A: We have to find tangent plane equation and normal line.

Q: a power series. Use the 2n +1 Integrate the function as 00 E(- 1)". Maclaurin series sin x= (2n +1)!...

A:

Q: A function f is differentiable at a number a.. A. ... if lim f(x) = f(a), f(z) – f(a) B. ... if lim ...

A: topic - condition for differentiable function

Q: 1 dx (use trigonometric substitution) x/1+x6

A:

Q: 1. Find the values of x,4 and z that corvespond to the critical point of the funchion Z="f(x,4)= Sx?...

A: We have to find critical points of f(x,y).

Q: Calculate the limit or show it is nonexistent. ry²e lim (r,y)→(0,0) x² + 4y4

A:

Q: f f(w) = tan (3w), find f'(w). Use exact values. f'(w) =

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

Q: Evaluate the iterated integrals  ∫1 0  ∫1 0 dxdy

A: Given query is to find the value of the integral.

Q: Suppose that lim (x,y)→(3,1) f(x,y) = 6. What can you say about the value of f (3,1)? What if f is c...

A:

Q: use implicit to tind the eguation of the tangent line tothe Ealloming differentiation Curve at' the ...

A: Topic = Derivative

Q: Solve eX =9 for x. ... The solution is x (Type an integer or decimal rounded to four decimal places ...

A: Consider  ex=9

Q: 2x2 +2x-4 lim X→1 X-1

A:

Q: Differentiate. y= log (x +x) log (x +x) = D dx

A: We can solve the differentiation as below.

Q: Find the point (x,y), at which the graph of y = 6x + 6x - 5 has a horizontal tangent. 2 The function...

A: Topic = Derivative

Q: Consider the following. y = 3x3 - 27x2 + 9 (a) Find the critical values of the function. (Enter your...

A:

Q: Find the convergence set of the given power series: 2" x" n! n=1 The above series converges for < x ...

A: Given:   Limit equations is given

Q: For the function y - f(x)- 2x + 0: df at = d.x a. Find 4. f'(-4) = 96 b. Find a formula for a 1 df a...

A: Answer: a.) ddf(2x3+0) = 6x2 =f'(x)f'(-4) = 6×(-4)2 = 96   b.) y = f(x) = y = f(x) = 2x3 + 0y = 2x3 ...

Q: 9. Evaluate the integral J 4x2+9 1 dx

A: We can solve the integral as below.

Q: Write the equation of a sine function that has the given characteristics. The graph of y = x2, shift...

A: Given that: y=x2

Q: Find the indefinite integral in each of the following. Show all necessary solutions. (2x – 3)dx 2. V...

A: Given :∫(2x-3)dxx2+2x+2

Q: Evaluate the improper integral. 9. 3x²e* dx (Express numbers in exact form. Use symbolic notation an...

A:     ∫-∞9 3x2ex=3·∫-∞9 x2exdx=3x2ex-∫ 2xexdx-∞9=3x2ex-2exx-ex-∞9=195e9

Q: 10. Show that the function f(x, y, z) = 2z³ – 3z(x² + y²) satisfies the Laplace Equation, = 0

A:

Q: 11+11-12=

A: Given that: 11+11-12

Q: lim (3+ 2)

A:

Q: Given the graph of f, find any values of x at which f'is not defined. 1 -2

A: Graph of the function is given, we have to find the values of x for which f'(x) is undefined