Find the average rate of change of f(x) = 9x² – 6 on the interval [5, t]. Your answer will be an expression involving t

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A: According to question,Given Cylinder and planes,x2 + z2 = 4y = -1y+z = 4

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Q: (b) Given that f(x) = 8(x*) g (5) = 3 and g(5) = 5, find the value of f (5).

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Q: Question 1: Differentiate the functions. 3 a) f(x) = 1– 5x +x7 b) f(x) = (x³ + 4)²

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Q: Find the radius of convergence of the power series. (If you need to use co or -m, enter INFINITY or ...

A: Consider the power  series            ∑ an (x-a)n then Series will convergent if |x-a|<R , where ...

Q: Use the following results, if needed, to determine whether each series converges or diverges. uk con...

A: (a) To test the convergence of the series ∑k=2∞1kln k5-1k5, we will analyze the convergence of the s...

Q: 3pts) Find the equation of the tangent line to the graph of the function f(x)=x-Vx at the point (1,0...

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Q: a2/2 if l띠 3. Find vertical asymptotes, if any, for y = f(x). Find oblique asymptotes, if any, for ...

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

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Q: 3. a) Find the percentage error in computing u = Vx at x = 2.45, when x is 4 %3D b) | If Ax = 0.005,...

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Q: following: (a) y = \f(x)| (b) y = f (x) (c) y = JF(x). f(x) y = 2 3

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Q: 8. What is de x2+1

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Q: Using Figure 1, complete the following function. (-8, - 6) Figure 2 csce = 5/3 5/4 -5/3 -5/4

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Q: Question Define R as the region that is bounded by the graph of the function f(x) = + 2, the x-axis,...

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Q: Use the following results, if needed, to determine whether each series converges or diverges. If the...

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Q: Solve the components of the given equation of conic sections and sketch the graph: a. x2 + 4y2 – 6x ...

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

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Q: Find the distance between the points (distance formula) 3.(-1, 1/2), (3/4, -4) 4.(a, b), (c, 0)

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Q: 8-2x (f) lim- X-4 x -x-12 Vx² +16 –4 lim- (g) x' +8 lim x-2 x+2 (h)

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

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Q: Differentiate the function by using the definition of derivatives. f(x + h) – f(x) f'(x) = lim h f(x...

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Q: O g(x) = (3t+ 2) dl t %3D

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Q: Why is there a need to solve for integrating factors?

A: We solve easily by using integrating factors. 

Q: 6. Consider function f(x, y) = x + y – 4ry + 1. Compute all the critical points of the function, and...

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Q: 8. What is de x2+1

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Q: Find the point on the graph y=Vx+1 that is closest to the point (2, 1).

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Q: 5. Find the limit of lim x* +0-x

A: Topic = Limits

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

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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

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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...

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Q: Show whether the following series converges 1 1 1 +. 82 1 22 52 (Зп — 1)° using the comparison test.

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Q: /1 + dt and g(y) f(x) dx, find If f(x) g"(T/6).

A: We have to find value of g"(π/6)

Q: Find the nth Taylor polynomial for the function, centered at c. f(x) = In(x), n = 4, c= 5 (x- 5)4 12...

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Q: x' - 36 lim 6 x+6 Vx+11-4 lim x-5 lim- 2 2-x x² +6x+9

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Q: a. Show by means of slope that the four points (0,0), (-2,1), (3,4), and (5,3) are vertices of a par...

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Q: What is f'(x) given the integral function f(x) = cos Tud u? O f(x) = -2x cos( T) %3D O f(x) = -2x co...

A: The detailed solution is given below Thank you 

Q: x³dx (v²– 1)7 3.

A: In this question we have to find the value of Integration.

Q: Question 21 sin 3x Given: dxWhat is the appropriate formula to find the integral? cos2 (3x) (4- 3 se...

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Q: Evaluate the integral / V4x4 - 12r? +7 xdx A - {(2x?-3) /4x4– 12x?+7 - 2 In |2x?– 3 + V4x4 - 12x2+7|...

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Q: Use the graphs to evaluate the expressions below. |f(x) 8(x) 4 4 -1 2 3 4 5 6 -1 1 2 3 4 5 6 f(g(4))...

A: Solving the problem by finding the values from the graph.

Q: 9 10 handwritten

A: We have to find the derivative of the given function using the rule of derivative  

Q: Use the difference a+1 - an to show that the given sequence {an} is strictly increasing or strictly ...

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Q: Find an equation of the tangent line to the graph of the function at a given point. Do not use the l...

A: Slope of the tangent line of the function f(x) is the derivative of the given function . f'(x) = lim...

Q: 2. (a) Prove the following inequality n(n- 1) ,2, 120 (1+ 1)" 2 1+ nz + 2 for any n 2 1. (b) Show th...

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Q: Find the Fourier f (x

A: Solving

Q: Determine whether the series converges, and if so find its sum. 4k+2 7k-1 k=1

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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 ...

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

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Q: Is the series convergent or divergent? Prove in no more than two sentences. +oo - n T1-n n=1

A: ∑n=1∞ (πnπ-1n3)(series with increasing terms)limn→∞(πnπ-1n3) =∞-0  =∞