The graph of a function f(x) is given below. Use the midpoint Riemann sum with 4 sub-intervals to approximate the area under the curve over the interval [2,6]. 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 2 3 4 5 6 X

Q: If f(x) f'(x) = = x² S²³ to dt then

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Q: g. y = tan x h. y = t+√√2t+√1-5t

A: To find the derivative of the following functions.

Q: ate and classify all (by classifying the extrema, we mean listing whether locate any stationary…

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Q: -10 -8 -6 -4 -2. 9 55 40 -6 16 V 4 O 8 10 TERMATH Write the standard equation for the hyperbola…

A: given graph of hyperbola

Q: 4. Using Geogebra, draw the parametric curve, x = sin³t+cos³t; y = sin² t - cos²t,0 ≤t≤ 2n-

A: The given curve is,The given interval is,

Q: Find an antiderivative of the function f(x) = 5x - √x.

A: f(x)=5x−x

Q: (a) Find a power series representation for f(x) = (b) Use your answer in part (a) to evaluate the…

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Q: r = sin(20), r = cos(20)

A: Given that the polar curve

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Q: 8. Evaluate the definite integral. a. 6 e² + 18 e² + 18z dz

A: Since you have asked multiple questions in a single request so we will be answering only first…

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Q: Let f(x) = x if x ≥ 5 5 if x < 5 a. Find f(1), f(5), and f(7). b. Sketch the graph of y = f(x).

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Q: 2. Find an equation of the plane through the point (1,3,2) and perpendicular to the vector (-3, 1,4)

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Q: 2. f(x) = = 1 1+72) [0,4], n = 4 , 1+x²¹

A: The given curve .The aim is to find the area under the curve using right-hand approximation in the…

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A: The arc is any part of the Circu mference of the circle. The length of arc can be found by using the…

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Q: 1. A rock is thrown upward with a velocity of 20 meters per second. Its height, in meters, t seconds…

A: According to our guidelines, we can answer only first question (due to multiple questions). Kindly…

Q: If f(x) = 15 to dt then f'(x) =

A: Note:-Since you asked multiple questions according to our policy we can answer only first question…

Q: Four Calculus II students have solved I sin sin(x) cos(x) dx. Their solutions are below. Use what…

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Q: Find an antiderivative of the function p(t) = t³ - 2 I t.

A: p(t)=t5−t42−t

Q: Use the summation formulas to rewrite the expression without the summation notation. S(n) = k = 1…

A: The given series

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Q: Determine the value of the following definite integral. St dz 15x+20x³ 3x²+2 Leave your answer in…

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Q: Consider the function f(x) = 3 cos x - 8 sin x. Let F(x) be the antiderivative of f(x) with F(0) =…

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Q: Find the solution of 4x²y" - 6x²y + y = 0, x > 0 of the form Y₁ = x¹(1+₁x + €₂x² + 3x³ + ...) Enter…

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A: The integration of acceleration function gives velocity

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Q: Given the definitions of f(x) and g(x) below, find the value of g(ƒ(8)). f(x) = X 11 g(x) = x² + 7x…

A: The given functions  and .The aim is to find the value of .

Q: how that the function is increasing on the given open interval. (Enter your answers as a…

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Q: Determine whether the series is absolutely convergent, conditionally convergent, or divergent. 4n²+3…

A: The given series By Root Test If L&lt;1 then series convergent If L&gt;1 then series divergent If…

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A: Let .To find the differential  when .

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Q: 15 x² 3x 54 (Round the answer to four decimal places.) Find the area bounded by y = X- -, x = 3, x4,…

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Q: 3 x¹ +1 dx

A: The given integral is (x4+1)/x2, limit from 1 to 3.

Q: The position of a particle moving along a coordinate line is s=√52+4t, with s in meters and t in…

A: The position of a particle moving along a coordinate line is s=52+4t, with s in meters and t in…

Q: ∞ 4. Apply the Ratio Test to the series [ the limit lim n→∞ (3n)! n=12¹ (n!)3 an+1 an and find

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Q: The compound amount, A, accrued with continuous compounding is given by A= P.100.4343rt, where P is…

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Q: At what value(s) of x on the curve y=-7+90x^3-3x^5 does the tangent line have the largest slope?

A: y=-7+90x3

Q: 10. Find a function f such that F = Vf and evaluate ScFdr along the given curve C • F(x, y, z) =…

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Q: 2x 1) Calculate the derivative of h(x) = √√e²x +e-²x

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Q: Find all relative extrema of the function. Use the Second-Derivative Test when applicable. (If an…

A: The objective of this question is to find the relative extrema of the function f(x) = sqrt(25 - x^2)…

Q: Determine a definite integral that represents the area of the region enclosed by r = 7 sin 0. •b…

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Q: Find an antiderivative of the function h(y) = 3y² — y6. An antiderivative is

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Q: At time t, the position of a body moving along the s-axis is s=13-1512+72t m. Find the body's…

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Q: Express your answer as a polynomial in standard form. f(x) = 2x² 5x – 12 - g(x) -2x + 2 = Find:…

A: f(x)=2x2-5x-12g(x)=-2x+2

Q: Suppose f(1) = 2, ƒ'(1) = 3, ƒ (2) = 1, ƒ'(2) = 4, and g(1) = 3,g'(1) = 5,g(2) = 1,g′(2) = 4. If…

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