Evaluate the limit using L'Hospital's rule if necessary 3 (+)* 1+ lim +-+00

Q: 4. x4 (²x²-x²³-1-1 + 0 dx

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Q: If what are the bounds of integration for the first integral? a= 11 [ f(a)d= = [ f(x) dx + " f dx […

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Q: please show all steps what are 2 critical points of the function: f (x)  =  esin(πx/20) −…

A: Consider the function f (x)  =  esin(πx/20) − cos(πx/20)

Q: 1. xaxy - 4y = x6 ex dy dx

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: (c) y = e-a sin(ax + 3). (e) y = tan(5x) 52+1 (d) y = a √a² + x²

A: (d/dx)(af(x)) = a(d/dx)(f(x)) , where a is constant. (u.v)' = u.v'+u'.v (u/v)' = (v.u' - u.v')/v2

Q: 2. Calculate the Jacobian of the coordinate change (x, y, z) to cylindrical coordinates (r, 0, z).

A: To calculate the Jacobian of the coordinate change  to cylindrical coordinates .

Q: Practice 4: a) Find at least the first eight derivatives of pattern you observe. sin.x and observe…

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Q: Show that the function y= x ln x is a solution of the differential equation xy" - y' + (1/x) y = 0.

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Q: Given the function ƒ, evaluate ƒ(−1), ƒ (0), ƒ (2), and ƒ (4). ƒ(−1) = Number f(x)= { x²-1 4+x-6| if…

A: The given function is

Q: X = +²37₁ y = + ²3² Find the values of + that correspones to vizontal vertical tangent lines to the…

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Q: 5. Find the outward flux of the field F = xzi+yzj+k across the surface of the portion of the sphere…

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Q: Find the surface area of revolution about the x-axis of y = 7 sin(2x) interval 0≤x≤ ka 2 over the

A: To find the surface area of revolution about the -axis of over the interval

Q: You are constructing a cardboard box from a piece of cardboard with the dimensions 2 m by 4 m. You…

A: We are given a cardboard with dimensions .

Q: 3 4. y sin³ 4x cos 4x =

A: The given function To find:-The integral in terms of sine function

Q: A ball of radius 15 has a round hole of radius 8 drilled through its center. Find the volume of the…

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Q: Rewrite 243-7x and 1 81 17x 13 in the form 3kx

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Q: 23-28 (a) Find the intervals on which f is increasing or decreasing. (b) Find the local maximum and…

A: (a) To find the intervals on which f is increasing or decreasing, we need to analyze the derivative…

Q: Which of the following are solutions to: 2 ln x² - ln x + 2 + C x² x+2 In + C x4 (x + 2)² O2ln |x|-…

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Q: Evaluate the double integral [[ (zy + 2) dA, where D is the set of points contain within the corner…

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Q: If y = 5x + 8 find 8' X dy dx at x = 1.

A: y=5x+8/x8

Q: a. Find the linear approximation for the following function at the given point. b. Use part (a) to…

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Q: C T 3 2 1 To find the blue shaded area above, we would calculate: b So f(x) dx Where: 1 2 3 4 f(x) =…

A: We have to use the graph to find the integral substitutes and area  under the graph

Q: (b) Use Elimination by. Addition method 2x + y = 1 3x - 2y = 5

A: 2x+y=1⟶(1)3x−2y=5⟶(2)

Q: d Find ax(-3x-4).

A: We need to find the following derivativeFormula Used:

Q: (a) Estimate the area under the graph of f(x) = 1 + 2x² from x = -1 to x = 2 using three rectangles…

A: We have given that, the function is    , x = -1 to 2.(a) For n=3, we have the right Riemann sum…

Q: Find the open interval(s) where the function is changing as requested. Increasing; y=√√x² + 10

A: y=x2+10

Q: Find the indefinite integral [³√5 + i* di

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Q: Find the critical points of h(x, y) = 3x² - 6xy + y² + y². Classify the critical points using the…

A: I have appended the formula used in the solution procedure

Q: Find the open intervals where the function graphed below is a) increasing, or b) decreasing. 10 -10…

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Q: The function f (x, y) = x³ - 3x² y + 3xy²-y3-11 22-2xy +49 y2 - 16 x + 208 y + 131 has a critical…

A: In this question, we will solve the all parts.

Q: Find the volume of a solid obtained by rotating the region bounded by the curve y sin x and the line…

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Q: 94. Can you have a finite absolute maximum for y = ax²+bx+c over (-∞, ∞o)? Explain why or why not…

A: The quadratic function standard equation is

Q: Use the graph to find the following limits and function value. a. lim f(x) X→2 b. lim f(x) X→2* c.…

A: In this question, we will find the limit by using the graph.

Q: Practice 3: Use the Quotient Rule to differentiate the function f(x), and then use the trigonometric…

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Q: Let g(x) = 2x² - 216x. Find the relative maximum and minimum values of g. Also find the intervals on…

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Q: 16. x1 + 3x2 +4x3 = 0 3x1 + 8x2 + 7x3 = 0

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: Let g(x)=2x²-1. (a) Find the average rate of change from - 1 to 8. (b) Find an equation of the…

A: g(x)=2x2−1

Q: 5. 13: I can estimate the value of a definite integral using a table, Riemann sum, or technology. A…

A: I have appended the formula used in the solution procedure

Q: Let C be the curve y = 3x³ for 0 ≤ x ≤ 1.6. 12 11 10- 9 8 Do 7 6 5 4 3 2 1 0.5 15 Find the surface…

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Q: To find the arclength of y = 3x² + 5 from x = 0 to x = 5, which is the correct integral? OL= 45…

A: Given that the curve we have to find the arc length of the curve between x=0 to x=5

Q: Find a graph up and down from the equation g (x) = (x + 1) (x-2 )

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Q: Determine the velocity of progress with the given equation: D = 20t + 5/t+1 when t = 4 seconds.

A: We have to determine the velocity of progress with the given equation:  when t = 4 seconds.

Q: Approximate the change in the volume of a right circular cylinder of fixed radius r = 21 cm when its…

A: The radius of the cylinder Let the height of the cylinder = hcm

Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (If the…

A: Consider the sequence

Q: Knowing that sin(0.65) is about 0.6, find cos(0.65). What relationship between sin(0.65) and…

A: sin(0.65) = 0.6

Q: Consider the function INTERMEDIATE WORK Using calculus give a sketch of y. Make sure you include the…

A: The given function equation is

Q: 5. T/2 Consider f/² secx tan x dx. (a) Explain why this integral is improper. (b) Determine whether…

A: I=∫0π/2sec⁡xtan⁡xdx

Q: Graph the function hoo-x-30 0x30 30x50 0.5x-65 i x>50 Choose the correct graph below OA 1530456075…

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Q: Find dx² 2 y=√x

A: Given

Q: Express each function as a composition of two functions. (Find f(x) and g(x) such that the given…

A: We have to write the given function as a composition of two functions.