S= Evaluate the integral r² dr 25 - x² using trigonometric substitution.

Q: Let where we don't know the base a. However, we do know that Use this information to compute L(x) =…

A: We have to find the values of given L(x).

Q: Would I take the gradient of each A and phi, then find them at the point given before dotting them??…

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Q: V. SA/9623/2-4,1¹/2 dx

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Q: Determine whether the improper integral converges and, if so, evaluate it.   ∞ 0 5x dx (3 + x2)2

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Q: Differentiate the function.

A: y=3ex+8x3 Differentiating with respect to x…

Q: rdp-(p+pr) dr = 0

A: Given :rdp-p+prdr=0

Q: Evaluate lim 1-cos3x x→0 tan 2x

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Q: 2. Evaluate the following integrals a) f √1+2-√1-dx (Hint: Maybe you need to rationalize the…

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Q: Use a grapher to find all local maxima and minima and the values of x where they occur. Give values…

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Q: Q₁. Find the angle between every two vectors below ( Vote b) f-3i+2k and g=4i+4j-2k

A: In this question, we need to find the angle between two vectors.

Q: Decide which of the following are true. Choose all that apply. Review intersections and unions here.…

A: Operations on Sets   Union of Sets If set A and set B are two sets, then A union B is the set that…

Q: Find the second derivative of y = e²x sin(3x)

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Q: Let u, ER" prove that |uv|≤|||||||||

A: This question can be solved using the following conceptsa. Dot product of two vectorsb. Modulus of a…

Q: Use the graph of the function to find its domain and range. Write the domain and range in interval…

A: We have to find domain and range of a function from it's given graph.

Q: x² - 10x x-0 9x²-x (d) lim

A: Given query is to find the limit of the expression.

Q: Estimate f′(6) for f(x)=2^x. Be sure your answer is accurate to within 0.1 of the actual value.…

A: Given function:- fx=2x

Q: A. A. Find if x = 2t4 - 4t² and y = t4 - 4t. dx t²-t+1 2t(t+1) B. t² +t+1 2t(t+1) Find f'(t) if f(t)…

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Q: Solve the given initial value problems. y'' - 4y' + 4y = 0, y(1) = 1, y'(1) = 1

A: To find out the solution of the differential equation.

Q: Qs Find the limits below ( a) lim(x,y)-(0,0) x2+y² 4xy²

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Q: Find the volume V obtained by rotating the region bounded by the curves about the given axis. y = 5…

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Q: onsider the following. f(x) = x³ - 3x² + 8 (a) Find f'(x) and f"(x). F"(x)

A: Solve for the derivative

Q: What is the solution of 3x² + 6xy2 + (6x²y + 4y²) y = 0 ? O 3x³ + 9x²y² + 4y³ = C O 3x² + 12x²y² +…

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Q: Find the curl of the vector field F(x,y,z)=x^2yi-2y^3zj-3zk.   A. curl F = 2y3i + x2k          B.…

A: Option (c) correct  For detail...go through the solution

Q: Find the indicated derivative using implicit differentiation. e²t_st = 6; dt " ds

A: Topic- implicit differentiation we are given ,es2t-st=6we know that(uv)'=uv'+vu'(eu)'=euu'where u…

Q: Use the given function value and the trigonometric identities to find the exact value of each…

A: Topic = Trigonometry

Q: 2) Consider the equation x² + y² = 100. Suppose that x and y are both functions of time t. Find…

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Q: 3

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Q: U Substitution (a) State the Substitution Rule. Explain its connection to the Chain Rul- (b)…

A: Topic = Integration

Q: 2-y If x = 32, find 2y 4. y+2 2y√ √2y B. dx B. Find y' if y = 4x-1 y-2 2y√ √2y (2x²-3)(3x+2)…

A: We can answer both the question in the below steps.

Q: EXAMPLE 5 Find an equation of the tangent line to the parabola y=x²- 8x +9 at the point (2, -3).…

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Q: Sketch the graph that possesses the characteristics listed. f is concave down at (1,4), concave up…

A: Given,   f concave down = (1,4)   f concave up = (9 , -6)   inflection point = (5 , -1)   graph

Q: f(x) = Answer: 1-cos(4x) 1+cos(4x) 2 sec² (2x)

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Q: Find the differential equations of every families of curves given 1. All parabolas with axis…

A: In conic section, there are four forms of parabola (up and down, left and right). The equation for…

Q: The chord of the arc subtended by 5°03'25" will vary in length with the radius. Which of the…

A: Sketch the schematic diagram of given question.

Q: What is the sum of the first 50 terms of the series 10 + 85 +160 + 32

A: Given :   series 10 + 85 +160 + 325   Common Differences

Q: Rewrite each of the following as a power function in the form kx", or state that it is not a power…

A: Given, 5x3;x3;72x

Q: If a ball is thrown into the air with a velocity of 42 ft/s, its height (in feet) after t seconds is…

A: We have to find the velocity when t = 1 second.

Q: < For y = 174√√x, find dy, given x = 9 and Ax = dx = -0.14. dy = (Simplify your answer.)

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Q: In problems 19-28, represent each repeating decimal as a series using the sigma notation. 19.…

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Q: Find all values of where the graph of f(x) = 2x³-39x² + 240x-5 has a horizontal tangent line.…

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Q: Use an appropriate table of values to find lim h->0 b^h-1/h where b = 48, accurate to four…

A: The given limit limh→0bh-1h We need to find the limit for b=48

Q: Consider f(x)=5x-3-41/x^2 Which of the following does the x-intercept of the tangent line at x=2…

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Q: If x= find dx y+2 2y/2y 4. B. B. Find y' if y = (2x2-3)(3x+2) 4x-1 48x³-2x²-8x+15 (4x-1)²…

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Q: Use PMT= 3¬ to determine the regular payment amount, rounded to the nearest dollar. The price of…

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Q: Evaluate the integral. *π/4 [" sin ³(x) dx

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Q: 29. xyy' = 1 + y²; when x = 2, y = 3.

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Q: A bus company is planning a trip for at least 107 people. If 107 people sign up, the company will…

A: using double derivative test to find maximum revenue

Q: 2 1. Find y' of tan(x²y4) = 3x + y²

A: The given differential equation is tan(x2y4)=3x+y2

Q: Write a in the form a=a+T+aNN at the given value of t without finding T and N. r(t) @ = (?)i + (x +…

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Q: -2 1 1 -1 -3 1 -2 are operations R2 = -2R1 + R2 and R3 = 3R1 + R3 used to convert the 2 and 3 in the…

A: We can find two row operations.