518 SHOW ALL WORK Aau aາq JV Find the exponential function given by f(x) = Ca that models the data shown in the table below. x 0 1 2 3 f(x) 2 18 54 ar

Q: Consider the series (3x)" n n=1 Find the interval of convergence of this power series by first using…

A:

Q: Find a general solution. Show the steps of derivation. Check your answer by substitution. -1.2 6. y'…

A:

Q: If f f(x) dx = 12, then ff(4x) dx is equal to If f f(x) dx = 12, then fx f(x²) dx is equal to

A:

Q: F (y)= 2 y-3

A: The given function is  F(y)=2/(y-3).

Q: - (lim 11100 ce 1500 = 0)

A: Given limit function :-  f(n) =1500/2n   To check given function is continuous or not

Q: Jc = − xj; P(−2, −4), Q(-2,-2)

A:

Q: Evaluate the definite integral. NOTE: Enter the exact answer. 12 5.² 11 |ti + t²j||dt 0 = =

A:

Q: Describe the graph of the equation. r = 3 sin 16t i - 3 cos 16t j O It is an ellipse in the…

A:

Q: 2. Show that F is a conservative vector field and then use that fact to evaluate SF. dr along the…

A: We need to show F is conservative vector field.

Q: 32-37 FOURIER INTEGRALS AND TRANSFORMS Sketch the given function and represent it as indicated. If…

A:

Q: Evaluate the triple integral zdV where E is the solid bounded by the cylinder y² + z² = 64 and the…

A: Here, to evaluate: ∫∫∫Ez dV where E is the solid bounded by the cylinder y2+z2=64 and the planes…

Q: For the given function sketch the graph; determine if f is continuous at xo and determine if f is…

A: Given: Graph:

Q: We can prove that if D is a region bounded by a simple closed path C in the xy-plane, then the…

A:

Q: 5. Find the work done by F = (x² + y)i + (y² + x)j + ze²k over the following paths from (1, 0, 0) to…

A:

Q: Express the integral as a limit of right endpoint Riemann sums. Do not evaluate the limit. 4 Sª √5 +…

A:

Q: Use a triple integral to find the volume of the solid shown in the figure. z = 16 - x² - y² 10 Need…

A:

Q: 8 765 4 3 2 1 -7-6-5-4-3-2 4 -2- -3 Clear All Draw: 4 -3 -6- 1 2 3 4 5 6 7 8

A:

Q: Solve the differential equation: (D³ + D)²y = 0

A: The solution for the given differential equation is

Q: Find the work done by the three-dimensional inverse-square field 1 F(r) = r on a particle that moves…

A:

Q: 1. Show that F is a conservative vector field and then find a function f such that F = Vf where F(x,…

A:

Q: 1 find the total differential dz. z=xsin y + x² z = (2x² + 3y)² z=5x-7y

A:

Q: Express the limit as a definite integral on the given interval. n lim [7(x)³ - 5x;*]4x, [2,7] n→∞ =…

A: Here, the limit of the integral is [2, 7]. Further, ∆x is replaced by dx and replace xi* by x. Thus,…

Q: Watch help video Answer all of the questions below about the function f(x) graphed below when x =…

A:

Q: Find the area of the part of the circle r = 5 sin 0 + cos in the fourth quadrant. Answer:

A:

Q: II. Find an equation of the plane containing the points (0,2,-1) and (1,-1,-1) and perpendicular to…

A: we have to find the equation of plane.  Let, a,b c are the direction ratios of required plane 1.

Q: d [r₁(t) · r2(t)] = [r₁(t) × r₂(t)] : = d

A: Given: r1t=costi+sintj+8tkr2t=7i+tk

Q: Find the integral of the following equation integrate cos(x + pi/3) dx

A: Given problem:- Find the integral of the following equation integrate cos(x + pi/3) dx

Q: Find the two x-intercepts of the function fand show that f(x) = 0 at some point between the two…

A:

Q: Find the indefinite integral. (Use c for the constant of integration.) [₁4 (4t³i + 14tj - 6√tk) dt

A: Here we have to use the concept of the indefinite integration.

Q: use the constrained variation to maximize the volume of an open cone when the surface area is 2π

A: use the constrained variation to maximize the volume of an open cone when the surface area is 2π

Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 ≤ t ≤ 1. √(x + 3y²) dy

A:

Q: Express the series using sigma notation 5-10 + 20-40+80 °5(-2)-¹ 21 -2n-5 7-1 0-5(-2)-1 -2(5)-¹ 7-1…

A: Infinite series

Q: Solve y"+y' + y = 6sin (2x) supo

A:

Q: Find all solutions of the equation in the interval [0, 21). csc 0 7 3 If there is more than one…

A:

Q: Direction: Find the integral of the following functions: 1. (5 cos x + 7 sin x) dx 2. f(3tan² x +…

A:

Q: Determine the sum of the following series. 31 10 Σ(1)

A:

Q: 4. sinx 1-sin² x dx

A: integration

Q: Find the area between the loops of the limacon r = Area = 5(1 + 2 cos 0).

A: We have to find the area between the loops.

Q: Find the limit. Use l'Hospital's Rule where appropriate. If l'Hospital's Rule does not apply,…

A:

Q: 1/2 y = (4x-3)¹/²₂ d³y 3 dx

A: Third derivative id given.

Q: Find the limit. lim (t i 6 j + t² k) t-5 lim (t i − 6 j + t² k) = i t-5 i+ i j+ i k

A:

Q: Find the indefinite integral. (Use c for the constant of integration.) [ (41²³1 (4t³i + 14tj - 6√tk)…

A: Given that we need to solve the indefinite integral with using integral constant C.

Q: Suppose that the revenue in selling x tables is equal to 200x – 0.25x“ dollars, and the cost of…

A: Here is the solution:

Q: Prove the identity. sin 2, x = 1- cos x 1 + cos x Note that each Statement must be based on a Rule…

A:

Q: Evaluate the vector-valued function at each given value of t. (If an answer does not exist, enter…

A:

Q: Solve for the solution of: (D3 + D)2y = 0

A:

Q: Evaluate the integral 13 ƒ(x)dx geometrically for ƒ (x) = { |3 − x ; x ≤ 5 2; x > 5

A:

Q: Given: xy =tan(x - y). Find dx/dy. tan² (z-y) soc²(z-v) +tan² (z y) sec (x−y) -sec² (2-y)-z 當…

A: find derivative dxdy from equation xy=tanx-y

Q: Homework 12 Polar: Problem 2 The limacon r = 1+ csin(0) has an inner loop when |c| > 1. (a) When c>…

A:

Q: Evaluate [x²z dx - yx² dy + 7 dz along the curve C shown in the figure. с 4 X [x²zdx - yux²2 dy +7…

A: