Evaluate the following * Sete e7x-³dx O e^(7x-3)/3 + C O e^(7x-3) + C - e^(7x-3)/7 + C O e^(7x-3)/7 + C

Q: Q3/ Use the definition of derivative to find f'(x) where fx=- 3 X+1

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Q: 2. Evaluate all of the integrals. b. 2|x - 21 dr

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A: The initial point is (3, -5) and the terminal point is (8, 6)

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A: In this question, we will evaluate the given limit expression.

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Q: Find the average value of f(x) = -3√x+ 5x over the interval [0, 3]. Submit an exact answer using…

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A: To find the integral , ∫π/2π∫0t  sin(4t-u) du dt

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Q: [x³ In 4x dx A) _ x4nux - A x +C oA nixt dx4+c 4x 16 B) In 4x xr…x4.C D) =xAndx- +x4+C

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Q: 2. Evaluate all of the integrals. b. ». 2x - 21 da

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A: 1+y2 dx+x2y+y+2xy dy=0

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A: We need to evaluate the following triple integral ∫12∫tt2∫0lnsteudu ds dt

Q: 3 Evaluate: ³₁₂₁(4x²y — z³) dz dy dx

A: Topic = Integration

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A: Given

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Q: ) Find the volume of the solid formed by revolving the region bounded by the cu y = √9-x² and y = 0…

A: Topic:- application of integration

Q: explain

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Q: 3 Evaluate: ³₂²₁₁²[z³(x + y)³] dz dy dx

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Q: e slope of the graph at the points (x₁, y₁) and (x2, Y2). - slope = , slope = y X -4 -3 4 3 2 (X₁,…

A: Topic:- geometry

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Q: 2 t √3u Evaluate the integral: №³4 524 4²2 ds du dt s²+u²

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Q: Find the area of the region bounded by the curves 1 y 5, y = 4 and the x-axis using vertical strip.…

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Q: Evaluate the integral: -2e 2е π/3 ₁² /³ tlnu tans ds du dt 0

A: In this triple integral we first integrate with respect to 's' then with respect to 'u' and in last…

Q: 4 Find the area of the region bounded by x = 2y²+1 and the y-axis using the horizontal strip.

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Q: Find the average value of f(x) = -3√x + 5x over the interval [0, 3]. Submit an exact answer using…

A: This question can be solved using the concept of average value of function over an interval.

Q: A particle is moving along a horizontal line such that its velocity in m/s is given by v(t) = 2t² -…

A: Please refer to the image below

Q: ¹₁¹+x² x + 2y dy dx -12x²

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Q: Find a number in [0, 1] such that the difference of one third the number from its cube is minimized.…

A: Let the number be x. Let f(x)= x³-x/3 So, f'(x)= 3x²-1/3

Q: Find the area of the surface obtained by rotating the curve y = cos(2x), 0≤ x ≤ π/6, about the…

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Q: 10. Consider the function f(x)=2x^2 +(0.4)x If the constant of integration is C=7.2, what is the…

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Q: cos x(sec x + tan x)dx

A: Given ∫cosx(secx+tanx) dxTo evaluate the integral:

Q: s s² s² sln teu du ds dt

A: We have to solve multiple integration.

Q: Consider the function f(x)=2x^2 +(−4)x What is the value of the constant of integration such that…

A: Topic:- application of integration

Q: Use the first principles definition of the derivative to find f'(x) where f(x) = √x

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Q: Evaluate: ₂₁(4x²y — z³) dz dy dx-

A: ∫03∫-24∫104x2y-z3dzdydx

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A: Topic = Integration

Q: hat is the concave up and concave down?

A: In terms of the second derivative Concave Up, Concave Down, Points of Inflection,  The graph of y =…

Q: I. Evaluate the following limits. 1. lim sinh r → r r→0 sinhr – r

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Q: For the following system: a) Determine how, if at all, the planes intersect. b) If they do,…

A: Given

Q: se local linear approximation to estimate In (0.99).

A: topic- linearization of a function

Q: Find the dimensions of the rectangle of maximum area that can be formed from a 10-m piece of wire.…

A: We have to find the dimensions of the rectangle of maximum area that can be formed from a 10-m piece…

Q: 1. Let f(x) = sin²(x) cos(x) g(x) = sin² (x) cos² (x) h(x) = sin² (x) cos³ (x) ㅠ (a) Plot all three…

A: Disclaimer: “Since you have asked multiple questions, we will solve the first question for you. If…

Q: S √x²-25 dx X

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Q: x 4 dx (x²+4)² S

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Q: 3 Evaluate: ³₂²₁¹ [2³(x + y)³] dz dy dx

A: This is a problem related to triple integration. Based on the general formula and concept we will…