For Problems 41-44, let h(x) = f(g(x)) and k(x) = g(f(x)). Use Figure 3.21 to estimate the derivatives. svijob

Q: Use comparison with f 1/(x² + 1) dx to show that Σ 1/(n² + 1) converges to a number less than or…

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Q: 1. (a) Write a Riemann sum approximating the area of the region in Figure 8.13, using vertical…

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Q: Use undetermined coefficients to find the particular solution to y"-2y'-15y = −1224 sin(3t) Y(t) =

A: By using undetermined coefficients to find the particular solution to the following differential…

Q: b) series converges or diverges. 8 n=1 1 (2n)! n=1 use the ratio test to decide whether the nen

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Q: Show the following example with different approaches: limx→0 (sin(2x) cos(x−2) )

A: To find :-

Q: b) Find ܣ n=1 the value of the following sener use partial fractions. 6n+9 (n² +3n) ² 2

A: series

Q: Calculate sin 37◦ accurate to three decimal places using a Taylor approximation. Check your answer!

A: Sin(37 degree) Find the value of Sin( 37 degree) by Taylor approximation.

Q: Which of the series in are power series? a) 1 + x + (x − 1)² + (x − 2)³ + (x − 3)4 + ... b) x²+x+2

A: The general form of a power series is  and a power series has infinitely many terms.

Q: Q2 Find the inverse matrix of: 1 3 5 2 2 -4 3 1 -2 5

A: To find the inverse matrix of the following matrix.

Q: 8. Explain how you would usethe root test to determine if the following series is convergent. Σ(2)…

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Q: The total surface area S of a right circular cylinder is related to the base radius r and height h…

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Q: 2x-8 If f(x) = and f(-2) = what is the value of B?

A: A function with one unknown (B) and the value of the function at (-2).

Q: I have the following question:  we need to find cosh(t)+sinh(t)= (et-e-t)/2 + (et+e-t)/2, I get…

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Q: = 6 cos(t) — 3 sin(2t), y = 7 sin(t) with 0 ≤ t ≤ 2π. Find the area of the region enclosed by the…

A: Let the curves denoted by x and y which are the function of t Then the area under the curves is…

Q: graph in polar using: 1.symmetry about origin 2.symmetry about x-axis 3.symmetry about y-axis…

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Q: Use the method of reduction of order to find a second solution t²y"+3ty'-3y = 0, t>0 Given y₁(t) = t…

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Q: 3.1. Determine the response y(t) of the differential equation below d²t dt² dy + 2y = 2 where y(0) =…

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Q: How do we calculate the limit of limx→0  (sin(x))/(9x3), by using the Taylor approximation

A: limx→0  (sin(x))/(9x3)

Q: 100 2" (x+2)" 7.) Find the interval of convergence of the power series Σn=11 n

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Q: Solve the equations: a) y"+4y'+4y=0 dy 3 b) - ²y=x dx

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Q: the amount of microbes on a plate is given by: N(T) = 10T2 - 40T + 200 , 1≤ T≤ 20 where T is the…

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Q: t) Consider the initial value problem y" +9y = 0, y(0) = 3, y (0) = 0. a. Take the Laplace transform…

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Q: y"-2y' +24y=3sin(4x)+6cos (7x)

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Q: find the interval of convergence. α) Σ n=1 x2n+1 n!

A: Since you have posted multiple questions I can do first question as per our company guidelines…

Q: You may be familiar with Pascal's triangle: 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1, where each number is the…

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Q: Use senies to find the powen senies solution to the following differential equation. You do not need…

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Q: Sketch the region enclosed by the curves y = sin(x), y = csc²(x), x = A and x = 3π 37, and compute…

A: Sketch the region enclosed by the curves y= sin(x), y= cosec2(x),  and compute its area.

Q: 3. (4.2 #3) Find the general solution. y" + 8y + 7y=0

A: The given equation is; y''+8y'+7y=0

Q: 2. The lateral surface area S of a right circular cone is related to the base radius r and height √²…

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Q: Find the flux of the vector field F = (y, -z, x) across the part of the plane z = 3 + 2x + y above…

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Q: find the Invense a Laplace Thansform as Function of variable to fully simplity and show all your…

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Q: Solve 4y"+6y'-4y = 0, y(0) = 1, y'(0) = −7 y(t) =

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Q: Provide an appropriate response. Find the general solution for the differential equation y' = 7e³x…

A: Use integration to solve both questions

Q: 1 (sec hr)2 1+tan ha 6 B=? +0 B e² +1 da = A + ln- (sec hx)² dx = Apen B e²et letanhx

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Q: 12 ► 13 A river flows at 2 m/s. Juan's boat can travel twice as fast down the river as it can go up…

A: Note :- Since you have posted multiple questions, we will provide the solution only to the first…

Q: 16. A solid generated by revolving the region bounded by the curve yine and the lines = 1, e about…

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Q: Find the integral using the substitution u = 13 [112 cos (113) dt Enclose arguments of functions in…

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Q: decide the derivative of asin(bx),step by step.

A: Given function

Q: 3.) Find the sum of the following series: 5-4+1/3- 16 32 + 9 27 64 81 ·+·

A: 6−4+83−169+3227−6481+⋯

Q: 2. Use a calculator to complete the table of data values; then use the table of values to determine…

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Q: Suppose F(x, y, z)=(x, y, 42). Let W be the solid bounded by the paraboloid z = x² + y² and the…

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Q: graph the following functions  f(x)=3x-1    if x\le 0        -2x+1   if x\gt 0

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Q: 7.1) SG √x+. 1 √x ₁ dx

A: To evaluate the following integral.

Q: Use the n-term test to show the following series is divergent. Σsin n=1 n² +1

A: By using the nth-term test to show that the following series is divergent.

Q: Find the value of ou/ox and du/oy if u(x, y) = x² + y²-2x²y;

A: To find the value of   if .

Q: Solve y"+8y'+20y = 0, y(0) = 4, y'(0) = -20 y(t)=

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Q: 145 Q1 Find the area bounded by x=2, y=0 and y=x2 in form of: a) Area= ff dx dy b) Area=ff dy dx

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Q: Find dx dx y= 11 지2 S cos (1³) dt ㅠ

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Q: Use the graph of the function y=f(x) below to answer the questions. (a) Is f(-3) negative? O Yes O…

A: The given graph

Q: The entire graph of the function h is shown in the figure below. Write the domain and range of h as…

A: The entire graph of the function  is shown in the figure below.To find the domain and the range of…