5 on the interval [-4,4] x3 Find the average rate of change of g(x) = 3x2 +

Q: Use Green's Theorem to calculate (4z? - 3yz)dr + (3zy + Vy? + 6)dy, where Cis the circle (r – 1)2 + ...

A: Greens theorem

Q: Find the interval of convergence of the power series. (Be sure to include a check for convergence at...

A: First we find radius of convergence. Then find interval of convergence. 

Q: Find the perimeter of the triangle whose vertices are: 1. A(2,1), B(3, -5) and C(1, -3)

A: A(2, 1), B(3, -5) and C(1, -3) 

Q: Consider the series >. 1 1 and 1 n312 n=1 n3 + 6n n=1 Write an inequality comparing 1 1 to for n 2 1...

A: We know, n³+6n-1≥n³ for all n≥1    

Q: 22. Given the function f at the following values, 1.8 2.0 2.2 2.4 2.6 f(x) 3.12014 4.42569 6.04241 8...

A: Definite integration problem

Q: Classify the series as absolutely convergent, conditionally convergent, or divergent. (–1)k+1 k! (2k...

A:

Q: What is f'(x) given the integral function f(x) = cos(e“)d u? %3D O rm = 3x cos(e) O f'(x) = 3x cos O...

A:

Q: Calculate F. dS where F = (3xy°, xe", zª) S is the surface of the solid bounded by the cylinder y? +...

A: Let's find. 

Q: Given: 5x2 tan ( 3x) dx. If u=3x³, then the resulting integral is Jf(u) du. Find. 4

A:

Q: Find the equation of the tangent to the following curve at the point where x = 1 y=Vx

A:

Q: Using Figure 1, complete the following function. to V Figure 1 cose = r/u r/v u/v v/u v/r u/r O O O

A:

Q: Find the tangent plane of the surface z = f(x, y) at (0,0, 0) in which 3y f(2, y) = || cos /3 t dt.

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Q: The displacement of a particle on a vibrating string is given by the equation s(t) = 14 + sin(14xt) ...

A:

Q: Q1. Solve the question A. Graph the curve B. Find the x-axis intersection points (Limits of integrat...

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Q: The graph shown is f(x) = 2x2 - 2. What is the integral that defines the area under this line betwee...

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Q: 04) Prove that 1- Cos + x) = sin x, 2- (sin x +cos x) sec x = sec2 x %3D

A: We have to prove that following trigonometric identity.

Q: 5. The following data give approximations to the integral M = sin x dx. Jo ()- () N (h) = 1.570796, ...

A:

Q: Is the series convergent or divergent? Prove in no more than two sentences. +oo 1 n=1

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Q: (x + 1)2 and the line (x+1)?, 1, where a is the same constant. 4. Let Si be the area of the region b...

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Q: Using the (e- 6) definition, show that f(x) = 3x – 1 is continuous at point x = 1.

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Q: fx +1 3- ax? if x > 1 if xs1 2. f(x) = %3D

A:

Q: Classify the series as absolutely convergent, conditionally convergent, or divergent. (-1)*+1k! (2k ...

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Q: A diver launches themselves off a diving platform into a pool. The height, in metres, of the diver a...

A:

Q: Using Figure 1, complete the following function. Figure 1 csce = r/u v/u v/r r/v u/v u/r O O O

A:

Q: X = cos 2t, y = cos t, 0 <t<T

A:

Q: Prove that the function z is continuo:as everywhere but nowhere differentiable except at origin.

A: The given problem is solved below in detail.

Q: 3. S(x) = (x²/3 – 1)²

A: Given that fx=x23-12c. if f'x&gt;0 then function is increasing.if f'x&lt;0 then function is decreasi...

Q: CONTINυITY (c) The function f (x) is defined in the interval [-1,6] by 3-x, -1<x<2 f(x) ={ x - a, 25...

A:

Q: Differentiate. f(e) = e cos(e) sin(8) f'(e) = cos (0)sin(0) – Osin (0) +0 cos (0)

A: I have stated the used formulas in the solution

Q: Solve the following differential Equations

A: Given differential equation, x2+y2+1dx+xx-2ydy=0x2+y2+1dx+x2-2xydy=0 Formulas used, ddxxn=nxn-1ddxco...

Q: Consider (x8+ 8x5+ 16x2) ² -dx. Using u-sub

A: Given: - The integral is, ∫x2+1xxx8+8x5+16x22dx To find: - The values of k and n. By using u-substit...

Q: tan x 2. (a) lim e →号一 (b) lim sin (tanh 3x) エ→十0

A: limx→π2-etanx

Q: 2) Find the tangent to the curve y 2 tan at x 1.

A: A detailed solution is given below.

Q: Determine the composite function fog and gof. For each composite function state the domain and range...

A:

Q: 5x? tan( 3x³) dx. fu= 3x³, then the resulting integral is f(u) du. Find A Given: 4 A none of the cho...

A: Topic:- application of integration

Q: analytically

A: As per the guidelines we can solve 3 parts only. 

Q: Given: -dx. Using u-substitution and transformation of integrand, what is u and du? 3/x - 2x 3 (A) u...

A:

Q: Situation 3: Find the area enclosed by the graph of the curve x^2+8y^2+16 = 0, the x-axis, the y-axi...

A: according to our guidelines we can answer only three subparts, or rest can be reposted.

Q: B. Directions: Expand t Scoring Rubric: 3- The final ansv 2- The final ansv 1- The final ansv 0- No ...

A: = (12q+4r)12  Binomial Expression:(a+b)n =∑n=0nni a(n-i) bi(12q+4r)12:  a=12q, b=4r=120(12q)12-0(4r)...

Q: Please see the attached photo for the given and don't use the Transcribed Image Text because it's ch...

A: Given

Q: Compute the LU factorization of the following matrix. No row interchanges will be necessary. You can...

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Q: x²dx 1. J4 –x*

A:

Q: 2+ cos x 5 (b). Let g(x) = Find equations of the tangent and normal lines to the x sin x graph of y ...

A: First find the point corresponding to given value of x then take the derivative of function to get t...

Q: 2. Use the Intermediate Value Theorem to show that 2.x - 3 if – 3 0 has a zero on the interval [-2, ...

A:

Q: Evaluate

A: We will find f''(2).

Q: Use Gauss' Divergent Theorem to calculate F. dS, where F = (2x + sen (e+1)) i+ 3yj+ cos(z?)k and S i...

A:

Q: Je2x sec2(e2x+1)dx ktan (e2x+1) + C, find the exact value of K. If the solution to is equal to A B -...

A:

Q: The product of the current ages of Vanessa children is 360. If her oldest child is twice as old as h...

A: Suppose, Vanessa has 2 children, whose ages are 2x, x such that: x &lt; 2x  Given: x•2x = 360  So, x...

Q: 2. S csch-x coth x dx

A: Given: - The indefinite integral is, ∫csch2(x)coth(x)dx To find: - The solution of the given integra...

Q: Using Figure 4, complete these functions. P(-20, 21) Figure 4 sine = -21/29 20/29 21/29 -20/29

A: