Determine the following general antiderivatives. [3x (x²-5)³4x [Axe+²7 tan(+²7) dx 10 d. cos(x) sin(x) -dx sin(x)cos(x) 1+x¹ dx 10

Q: dw the functions w= -5x²-3y².x= cost, and y=sint, express as a function of t, both by using the…

A: Use chain rule for derivative

Q: 3 -7 [3] 7 -5 Let E= -2E= 0 Find -2E. 00 8 [000) 000 1000 [00] Undefined

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Q: Consider the following theorem. Theorem If f is integrable on [a, b], then [ºf(x) dx = dx = lim…

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Q: The average price of a two-bedroom apartment downtown New York City during the real estate boom from…

A: Given: The average price of the property from 1994 to 2004:

Q: Find the equation of the tangent line to the graph of f(x) = x³e-* at a = 0.

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Q: Find the extreme values of on [-2,2]. f(x) = ret, x < 0 2x³9x² - 12x, x ≥ 0

A: Solution of given question is written in below steps.

Q: A rotating light is located 19 feet from a wall. The light completes one rotation every 2 seconds.…

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Q: For the right triangles below, find the exact values of the side lengths b and c. If necessary,…

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Q: 2. Given f(x)= x³ + ax² + bx has critical numbers at x = 1 and x = 3, find a and b.

A: Given query is to find the value of a and b.

Q: (b) 3, 1, 1 1 1 3'9' 27

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Q: x²+4x+10 x3+2x²+5x dx

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Q: Show that the integral is independent of the path, and use the Fundamental Theorem of Line Integrals…

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Q: Find the indefinite integral using integration by parts with the given choices of u and dv. [x x cos…

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Q: مرده X dx (3x²-1)³

A: This question is based on definite integral.

Q: Let (3, 4) be a point on the terminal Find the exact values of cos 0, sec 0, cos ( = 0 sec 0 = 0 cot…

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Q: 8x³ + 4xy - y³ = 1

A: Given :

Q: 5. 39+5 dy (59-7)2

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Q: f(x) = loga x

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Q: ∫12v (7+6v2)9 dv Evaluate the following integral using substitution rule or integration by…

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Q: Use Green's Theorem to evaluate the integral. Assume that the curve C'is oriented counterclockwise.…

A: This is a problem related to vector calculus. Based on the general formula of green's theorem we…

Q: Use Newton's method to approximate a root of the equation 3z7 + 2z¹ + 2 = 0 as follows. 3 be the…

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Q: A circle has a radius of 11 ft. Find the radian measure of the central angle that intercepts an arc…

A: We can find the radian measure in the following steps.

Q: Find the area of the region enclosed by the graphs of x = y³ - 14y and y + 3x = 0.

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Q: Find the arc length L of the graph of r(t). r(t) = t3 i+t p j+126t2 k, 3≤t≤6

A: r(t)=t3 i +t j+126t2 kdxdt=3t2dydt=1dzdt=252 t3≤t≤6

Q: A farmer uses x lb of fertilizer per acre at a cost of $0.20 per pound, leading to a revenue of R =…

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Q: 2 Σ(-1)". n+1 n=1

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Q: 1. Use the limit definition of derivative (no shortcuts!) to find the derivative of f(x) = 3x² + 2x.

A: The formula for derivative of function f(x) using limit is given by:…

Q: Evaluate the definite integral. NOTE: Enter the exact answer. S||ti + 1²j|| dt = |

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Q: second derivative of y with respect to x from the parametric equations given 4) x=√1-t₁y = t³ - 3t…

A: We can find the required 2nd derivatives as below

Q: > Question 22 if y = log3 x find y' xina 01 2/xina

A: To differentiate..

Q: 5. If a function f(x) has the same value at the endpoints of a particular interval, will there…

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Q: Find the absolute extrema for the function f(x)=x+ on the interval 0≤x≤ 6.

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Q: Consider the following. y = √x 4 X = 8 y = 2-x -6 -8 (a) Form the integral that represents the area…

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Q: Find the area of the region lying to the right of x = y² + 13y + 14 and to the left of x = 5y + 2.…

A: Area bounded by the curves :  If f(y) and g(y) are two continuous function on a,b and f(y) ≥g(y) on…

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A: We have to find the value

Q: Question 15 Find the derivative of y = 32x+5 A. 2 ln 3 (3²x+5) B. In 3 (3²x+5) C. 2ln 3 D. 32x+5 O B…

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Q: The depth (in feet) of water at a dock changes with the rise and fall of tides. The depth is modeled…

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Q: The graph of g consists of two straight lines and a semicircle as shown in the figure. y 20 y = g(x)…

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Q: The estimated monthly sales of Mona Lisa paint-by-number sets is given by the formula q = 98e-3p² +…

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Q: Use the definition of a Taylor series to find the first four nonzero terms of the series for f(x)…

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Q: An airplane leaves City A and flies 144 km due north to City B. It then turns through an angle of…

A: The solution is given in the next step.

Q: sec7(t) tan(t) dt Evaluate indefinite anti-differen

A: We have to find the integral

Q: 3/3 10. Evaluate • 73 (x² +9)3/2 dx

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Q: Suppose that f is integrable on [-4, 7]. If the average value of f on the interval [-4,7] is 4.25,…

A: Given,             Suppose that f is integrable on -4,7. The average value of f on the interval…

Q: Show that the integral is independent of the path, and use the Fundamental Theorem of Line Integrals…

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Q: Find the volume generated by revolving about the y-axis the area bounded by the curve x^2 = 4(x-y),…

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Q: Use the given derivative to find all critical points off, and at each critical point determine…

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Q: xdx √9-4x²

A: Given,            ∫x29-4x2dx

Q: Consider the following. f(x) = 25 25 20 15 10 g(x)=x² 5 X -4 -2 2 4 6 i (a) Form the integral that…

A: We are given a shaded region bounded by functions  f(x) =25 and g(x) =x2 where x≥0 We have to  1.…

Q: A rectangular plot of land is to be fenced in using two kinds of fencing. Two opposite sides will…

A: A rectangular plot of land is to fenced in using two kinds of fencing. Two opposite sides will use…