Find the critical points and sketch the graph of the function. 1. f(x) = √5 + x 2. f(x)=x²-3x³ + 3x² +1

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A: Let's find value of given function.

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A: Let's find area of surface obtained by given curve.

Q: 5. Consider the region bounded by the function y = 4x, and the lines x = 0 and x = 3 Then the area…

A: We know  that the area under the graph of a continuous function f (x) between the vertical lines x =…

Q: Question 8 What is the equation of the line tangent to the function y = x³ + 7x² + 5x - 2 atx=0? Oy…

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Q: Given the polynomial function: h(x)= 3x³-7x²-22x+8 a) List all possible rational zeroes of h(x). b)…

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Q: Find all the second order partial derivatives of g(x,y) = x°y + 5 sin (y) + 4y cos (x). 20x°y - 4y…

A: Given query is to find indicated partial derivative.

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Q: Below is the graph of y=x. Transform it to make it the graph of y=-x-4-2.

A: a) y=-x-4-2b) y=-2x-4

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Q: Find the curvature of the curve F(t) = (cos(5t), sin(5t), 3t) at the point t

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Q: ) Find dw if w = xe³/², x = t², y = 1 — t, and z = dt 1 + 2t.

A: Topic:- application of derivatives

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Q: Determine the indefinite integral. 25 dx x In 7x 25 S= Sx157x x In 7x dx =

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Q: 2) 1 V1-x² dx

A: The given integral,      ∫11-x2dx

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A: Let's find given graph represent a function or not.

Q: Topic: Tangent Lines, Normal Lines, and Rates of Change

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Q: Using Wallis formula, find the integral of the expression. Answer in 5 decimal places (example…

A: We will use Wallis integral formula to solve this question.

Q: a²fa²f The two-dimensional Laplace equation + dx² = 0 describes the potentials and steady-state…

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Q: Let f(t) Find the Laplace transform F(s) by computing the following integral: 00 [ f(t)e=" dt = […

A: This question is related to integration, we will solve it using given information.

Q: 6. Consider the region bounded by the function y = 4x, and the lines x = 0 and x = 3. Then the area…

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Q: Question 5 What is the equation of the line perpendicular to the function y = x³ +7x² + 5x-2 at x =…

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Q: Find y' 1. (x-y)2 = sin x + sin y

A: Note: As per our guidelines we are supposed to answer only one question if there are multiple…

Q: Verify that af ?x || 224 ?х ду = 224 ду дх - for f(x, y) = 7x®y³ – 5x5y4.

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Q: The entire graph of the function g is shown in the figure below. Write the domain and range of g as…

A: We have to find out the domain and range