Given f(x)=x²-1 on [-2,2]. a. Find the critical numbers of f on the given interval. b. Determine the absolute extreme values of f on the given interval.

Q: The derivative of y with respect to a given ¹ = 1 is Oy' = yx²-¹ O y'= 0 Onone of the choices Oy' =…

A: I have stated the used formula in the solution.

Q: -3 -2 ²₁ ² [z³(x + y)³] dz dy dx

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Q: Explain why the function h is discontinuous at a = -2. 1 x = -2 h(x) = x + 2 1 x = -2

A: As per the company's guidelines, we are supposed to solve first question for you, kindly repost…

Q: Evaluate: √₂²³ Sª₁ S₁ (4x² yz — ) dz dy dx -

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

Q: Use the table of integrals to evaluate the integral. 2 5x³√4x² - x4 dx

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

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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: Find the volume of the solid generated by revolving 1 the region bounded by y = e¯x², the x-axis and…

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Q: Find the general solution of (d²s)/(dt²) + 2(ds/dt) + 5s = 0. OA.y = C₁e(t) cos2t + C2 e(t) sin3t…

A: Let's solve given diffrential equation.

Q: Q1/ Without using L'Hopital rule, find the following limit. √2+x-√2-x lim- ×-0

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Q: ع لح ل(۸ + ")APNPLPLg للع(۸

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Q: Prove that dx x(1+x²) 5 = lnx - 1²/2² (₁4²2²2) + ( C. +x²

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Q: You are given the polar curve r = 3 cos(0). (a) List all of the points (r, 0) where the tangent line…

A: We have to find the point for horizontal and vertical tangent lines.

Q: 3 -2 Evaluate: ₂₁ [2³(x + y)³] dz dy dx

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Q: Let R be the region below bounded by the graphs of C₁: x² + y² = 16, C₂: y = 4 − (x + 2)², and C3: y…

A: If you have any doubt feel free to ask.

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

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Q: Evaluate: du [(x²-y²)²1 ³₁ 1² du dt x+y

A: Given , ∫-13∫02x2-y22x+ydudt

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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: Do as indicated. a. Find the equation the tangent line and normal line to the graph of f(x) = x³ at…

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Q: elaborate pls, i could not understand the flow of the solution

A: We have to elaborate the solution.

Q: = 2 · and g(x) = √x² – 2x +1, then_lim [(ƒ(x) · g(x)] is z→1¹ If f(x) =

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Q: Does the following graph represent a function that satisfies the following conditions? f(0) = -2…

A: Here we need to cross check the given conditions are applicable to the graph of the function or not.…

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: What are the first 5 terms of the sequence represented by a=2n-3a n "n-1, where a₁ = 4₂

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Q: Given F(x) below, find F'(x). cos - Las () (1² - 2) dr F(x) =

A: Given.

Q: 3 Evaluate: 2₁ (4x²yz - 2 ) dz dy dx 4

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Q: Evaluate the indefinite integral given below using the indicated substitution. 1-20 -2(-2x + 9)³ dx…

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Q: Find the volume of the solid generated by revolving the region bounded by 2y = e-x², the x-axis and…

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Q: explain

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Q: -3 ³₁₂₁(4x²y - z³) dz dy dx

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Q: Determine the intervals on which the function is concave up or down and find the points of…

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Q: VI. Determine the instantaneous rate of change of the function √x sin (³) In 2 = = [X² f(x): dt 1 +…

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

A: Find the area of the region bounded by x= 1/(y2+1) and the y-axis using the horizontal strip.

Q: Evaluate the integral S (2x − 8)dx 2 - 6x + 18 x²

A: Evaluate the integral

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Q: Find the area of the region bounded by the curves y = 1 (x+6)²¹ į, y = = 4 and the x-axis using…

A: Explanation of the answer is as follows

Q: Determine the intervals on which the function is concave up or down and find the points of…

A: topic- inflection points and concavity

Q: -2 [(x² - y²)²] x+y Evaluate: ³₁² du dt

A: Since the integration is to be done with respect to u and t but the given function in the bracket is…

Q: The population of a municipality in the country varies according to the function…

A: Topic:- Algebra

Q: - Let v and w be vectors such that |v| = 2, ww = 36 and the angle between v and w is T/3. Calculate…

A: This question can be solved using the concept of vectors.

Q: t sin (=) dt du

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Q: Q4: Solve the follov A) Find and graph the volume generated by revolving the first quadrant area…

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Q: Evaluate: xy² dx dy S

A: Given: ∫04∫0yxy2dxdy

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

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Q: If the total cost function is given by TC=300+5q+(3)/(q2), what is the marginal cost when q=3?

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Q: Determine how the function f behaves at infinity. f(x) = (x³∕2x³) + (2/5x) -2

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Q: dentify the surfaces of the following equations by converting them into equations in the Cartesian…

A: The given data is: To identify the surfaces: z2=4+4r2

Q: Use the definition of continuity and the properties of limits to show that the function g is…

A: This question can be solved using the concept of continuity of a function at a given point.

Q: Evaluate the indefinite integral given below using the indicated substitution. /-20 -2(-2x +9)³ dx u…

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