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Q: 1. Determine the slope of the tangent line to the function f(x) = 2                                 ...

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Q: Determine whether the improper integral converges and, if so, evaluate it. (Use symbolic notation an...

A: The given integral,      ∫011dx11-x

Q: [sin (21x) dx

A: ∫sin4(21x)dx Note- sin2x=1-cos(2x)2 and cos2x=1+cos(2x)2

Q: answer

A: Please refer to the image below

Q: Use any method to determine if the series converges or diverges. Give reasons for your answer. 00 (-...

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Q: Express the repeating decimal as a fraction. 0.685828282828...

A: Given that 0.685828282828 Convert the repeated decimal as a fraction.

Q: Evaluate the ff Sinx d /sinx+ casx

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Q: Find A) The x values of all points where the function over the given interval has any relative extre...

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Q: Evaluate the integral. Show all your work. tan’ x sec xdx 3

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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: A particle is moring along ASit reaches to the point 2,6), the y-cordinate S decrea Sing ata rate of...

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Q: ) A spherical balloon is inflated with gas at the rate of 800 cubic centimeters per minute. How fast...

A: I am attaching image so that you understand each and every step.  

Q: Use the difference an+1 – an to show that the sequence {n – 2"}n=1 - is strictly increasing or stric...

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Q: integral f (z+1) e^2z  dz

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Q: Find the missing values assuming continuously compounded interest. (Round your answers to two decima...

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Q: If f(x) 3 sin '(2), then f'(x)-

A: Given that: f(x)=3sin-1(x5)

Q: A doctor prescribes 100 milligrams of a therapeutic drug that has decayed to 40% of its original qua...

A: We use radioactivity decay law 

Q: Simplify the expression sin (cos (300)), where the angle is measured in degrees. Do not include the ...

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Q: Find the differential of each function. (a) y = x2 sin(4x)

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

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Q: Find the slope of the tangent line. y = cos3x at x= -5pie/12

A: Given:     y = cos3x      At x = -5π/12

Q: 3. Below is his graph. Is his graph correct? If not, explain what mistake(s) he made. TO 8. Brian gr...

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Q: Consider the power series n°x8n 43046721" Find the center and radius of convergence R. If it is infi...

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Q: ydx + x(Inx - lIny - 1) dy = 0, when x = 1, y = e %3D

A: Given :     ydx+xlnx-lny-1dy=0,        when x = 1 , y = e that means y1=e

Q: Evaluate the integral. Show all your work. dx (x² – 1)3/2

A: Given that: ∫dx(x2-1)3/2

Q: A 16-foot ladder leans up against the side of a building so that the foot of the ladder is 6 feet fr...

A: topic - inverse trigonometric ratios

Q: Let f(x) = tan '(sin(2a)) f'(r)

A: Given :f(x)=tan-1(sin(2x))

Q: To the nearest tenth, what is f′(k) if f(x)=0.09e^xln(x) and k=8?

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Q: 1. Prove that the two sets of conditions are equivalent. Here, T is a linear transformation and u, v...

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Q: Use substitution to find the Taylor series at x = 0 of the function 15 sin (-x). ... What is the gen...

A: This question is based on Taylor series expansion of sinx .

Q: 3. The graph of f(x)= { 3, x≤-1     (x-1)2, x>-1 is shown below. Evaluate lim f(x) x→-1-. a. The li...

A: (3). The given function is:f(x)=3              x≤-1(x-1)2x>-1

Q: Use the difference an+1 a, to show that the sequence - {n – 3"}, is strictly increasing or strictly ...

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Q: 3. Find the volume of the solid obtained by rotating the region bounded by the curve y = x + 1, y=0,...

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Q: If f(x) = 2 tan '(5 sin(3r)), f'(x)-

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Q: Consider the following sequence: {a,) = {n – n²} Sn=1 Use an+1 - An to show that the given sequence ...

A: Calculus   sequence 

Q: lim (3+ 2)

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Q: Let g(x) = -1/x2. Evaluate lim g(x) x→0 by drawing its graph. a. ∞   b. 1    c. 0    d. -∞

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

Q: 28. 16(V1+x -1) lim

A: Topic = Limits

Q: What is the inverse laplace of 8/5 * L-1(1 / (s2 + 4))

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Q: 4- If the leng th of the edge of a cube IS Thcreasmg atarate of sem/s, hemtast is the volume of the ...

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Q: Evaluate the following expression. 1 arccos Report your answer as a simplified fraction. Provide you...

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Q: hi

A: 1232Now,32 = 2×2×2×2×2 =4×4×232 = 4×4×2 = 42

Q: A pole stands 75 feet tall. An angle is formed when wires of various lengths of aF feet are attached...

A: Given that length of a pole is 75 ft.  find the rate of change of the angle dθdx  at x=199ft

Q: The two functions x(t) and y(t) satisfy the simultaneous equations dx/dt - 2y = -sin(t), dy/dt + 2x ...

A: Given: dx/dt - 2y = -sin(t), dy/dt + 2x = 5cos(t)

Q: 3. Suppose a feather is dropped from a height of 40 m above the surface of the moon, its height s (i...

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Q: This question has several parts that must be completed sequentially. If you skip a part of the quest...

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Q: 20 Find the Maclaurin series for f(x) = - 1+x 20 What is the Maclaurin series of 1+x 00 Σ | (Type an...

A: We have to find the Maclaurin series for f(x)=201+x.

Q: Use the Root Test to determine convergence or divergence (or state that the test is inconclusive) of...

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Q: Let y be the part of the curve y = x² running from (-1,1) to (2,4). Calculate xy dx + (x + y) dy.

A: (1)

Q: Determine whether the series converges, and if so find its sum. 00 1k+2

A: Given that: ∑k=1∞4k+27k-1