Sketch the region whose area is given by the definite integral. хр y3 Use a geometric formula to evaluate the integral.

Q: 2 For the function f(x) = -x', find f'"(x), f'"(0), f'"(1), and f"(- 1).

A: To find the double derivative for the given function.

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Q: Provide what is asked for in each item. 23 with f'(x) = 3a (9 – a²) (9 – 3x2)2 54.x(x² + 9) (9 –…

A: Given problem:-     d. Make a table that shows the intervals where f is increasing or decreasing,…

Q: f(x) = 3 log(x) f(x) = 3 log(x) 1 103 1 102 1 10 1 10 102 y y 4 40 60 80 100 20 40 60 80 -2 -4 -4 y…

A: Given query is to sketch the graph.

Q: COLUMN A COLUMN B S(:-0) dx =-4 In\x| + C 4 In/x| + C 1. A. 4x B. 4* 2. dx 6Vx +C С. 4 3. S(3Vx +)…

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Q: Find the area under the given curve over the indicated interval. 10 y=x: (1, 3] The area under the…

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Q: 3. Find the area bounded on the right by x+y=2, and on the left by y=x and below by x-axis.

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Q: Suppose that , g(t) dt = v2. Find g(t) dt b. du а. -3 g(r) dr [-g(x)] dx d. с. -3 V2

A: Note:as student asked only part A,B so I solved as per requirement.

Q: Let E be the region bounded above by z? + y² + z² = 10² , within z? + y? = 4° , below by the r®…

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Q: x² + 4x - 4

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Q: dx 4. J 1+ Vx -2

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Q: 3. Evaluate the following integrals: Cose G = 1+ sin ở) v de Vsin

A: LetI=∫cosθ1+sinθsinθdθPut sinθ=udifferentiate on both sidecosθdθ=duI=∫1u1+uduPut u=v2differentiate…

Q: 1. Find the area between y=x and y=x' from x=-1 to x%-1.

A: Since mutliple questions are asked, I am answering the first question.

Q: -1)" =£ Given: In(1 + x) if x < 1. n + 1 n=0 (-1)" (n +2 2n+1(n + 1) 4. Compute the exact value of…

A: ln(1+x)=∑n=0∞(-1)nn+1xn+1     if x&lt;111-x=∑n=0∞xn  if x&lt;1

Q: 4: Show yor work. a) 1: Find the exact area of the surface obtained by rotating the curve y? +x =5,…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Solve the inequality. (Enter your answer using interval notation.) 4x2 - 16x 2 0 Graph the solution…

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Q: Find the vectors that satisfy the stated conditions. NOTE: Enter the exact answers using the…

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Q: 4. Consider the function f(x) = (2x - 3)5. Discuss the continuity and %3D differentiability at x =…

A: 4.f(x) = (2x-3)15 from the graph, f(x) is not differentiable at x=32 , since slope changes at x=32…

Q: Consider the graphs, shown below, of the functions f(x) (blue, first graph) and g(x) (red, second…

A: According to our policies we are allowed to give solution of only one question at time. For other…

Q: heorem 13.9 to find the directional derivative of the function at P in the direction of the unit…

A: Given query is to find the direction derivative.

Q: d. The curves y=x-4, y-8-2x.

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

Q: Evaluate the integral using the following values. x3 dx = 960, x dx = 24, 8. dx = 4 -5x dx

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Q: Complete parts (a) through (c) for the following function. f(x) = - 3x° + 3x² - x- 1 (a) Find…

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Q: 4. Fill in the blank with "all", "no", or "some" to make the following statements true. Note that…

A: Explanation of the answer is as follows

Q: 1 |sin xdx ーπ 3 sin xdx 5 S sin xdx

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Q: Two parametric equations are given by: x = cos (t), y = sin³(t) u = sin(t) , v = cos(t) In one…

A: Let's find.

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Q: Evaluate the following Integrals by part: 1- fx°e*dx

A: This is a problem related to integration of the function. Based on the general formula we will…

Q: Find the Taylor series centered at c = -1. 6. f(x) = %3D 3х- 2 Identify the correct expansion. 3"…

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Q: Find t6e eavation of tangent ine of fcx) = X+) at X=2 X-3

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Q: Use a calculator or computer to evaluate the integral. Round your answer to one decimal place.…

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Q: Match the expression in Column B to complete the statement in Column A. Input the letter that…

A: 3) To evaluate: ∫3x+3xdx Note that: ∫xndx=xn+1n+1+C

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Q: B side of cube = 10 cm (A. B); (C. D); (E.G);(G.B) ? (Ex F); (A x G) dan (Cx F) ? 2. what is the…

A: From the given figure we get A→ = 10i+10k B→ =10iC→ =5j+10kD→=5i +10kE→ =10i+10jF→=10kG→=10i+10j+10k…

Q: 2) The rate of change of an electrical current, i, in a microprocessor circuit is given by di 0.4t –…

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Q: In(1tcos 3x) 10. dx 1+cos 3x + C S (cos x)(sin?x)dx = 2 s In(3x) dx 11. + C 5in (1x) + C 12. %3D

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Q: Consider the function, whose graph y = f(x) is shown below. -3 -2 What is the set of values of x E…

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Q: 12 1 dx using a left-hand sum withn = 3. x + 5 Estimate Round your answer to three decimal places.

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Q: Find any critical numbers for f and then use the second derivative test to decide whether the…

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Q: 5 (5y, + 1.5y)3 16.036 (5 + 2/3.25y.) INIM

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Q: Find the equation of the parabola described below. Find the two points that define the latus​…

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Q: 2. Find the equation of the tangent line to the graph of y = 3cos 4x at x = 3

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Q: (a) Find an equation of the tangent plane to the surface at the given point. x2 + y? + z? = 14, (1,…

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Q: Find the gradient vector field (F(x, y, z)) of f(z, y, z) = e®2z + $y + 2= F(1, y, z) =

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Q: Consider the differential equation x² y" – 3xy' + 3y = 0. (a) Verify that y = cjx + c2x is the…

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Q: 3. A 1 000-metre track is to be built with two straight lines and semicircles at th below. Find the…

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