Evaluate the ff (show all steps) dx (4-x²) 3/2 √

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A: Firstly find  derivative of y then find length of curve

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Q: Problem 7 Proof that if lim f(x) exists then it must be unique i.e., x→a if lim f(x) = L and lim…

A: In this question, we want to prove that if a limit of a function exist then it must be unique.

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Q: x(t) Find a plane containing the point (-4,3,-8) and the line y(t) z(t) = 8 - 3t 7 + 4t -8+ t

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A: Here i have find the answer upto 4 decimal place.

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Q: The definite integral is equal to [²3x 3xdx Select one: O none of the others O 3 lò O3 lò xdx +3 lit…

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Q: 08 06 04- 02- }} ye y=0x=y² 02 yer* dxdy = 36 38

A: To switch the order of integration and then evaluate the value of integration.

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A: Hete we have to find the maclaurin series of f.

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A: This question can be solved using the concept of lines in three dimensional geometry.

Q: True or False: Suppose k is constant. Then 5 [² is equal to 10k. Select one: True O False kdx

A: Solve the given intregal

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Q: Q1/ A- Represent the following data in a graph using the bar graph method. temperature [ today] 27…

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A: Let's find intersect points.

Q: Problem 2 Solve y" - 25 y = x ex

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Q: True or False: We have Select one: True False -8 √xdx = 64 3

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Q: Brine containing 3 lbs per gal of salt enters a large tank at the rate of 2 gal/min and the mixture…

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Q: Exercise (c) Find the inflection point. Find the interval on which f is concave up. Find the…

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Q: he transformation from Cartesian to plane coordinates in x-direction is given by x=rsine x=rcos20…

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Q: Solve the equation. dx 2x1² dt **** An implicit solution in the form F(t, x) = C is =C, where C is…

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Q: 2 y=0x=y f(x,y) dxdy =

A: Solution given below

Q: Find the arc length of the curve below on the given interval. 3 1/3 3.5/3 y = 5x +9 on [1,27] The…

A: The given curve,    y=35x53-34x13+9 on 1,27

Q: Problem 5 Using Laplace transform, solve y" - 4y + 7y = 0 y(0) = 3, y'(0) = 7

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Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) ● (esti -j+e-6tk + lime⁹ti…

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Q: Evaluate the following limit. Use l'Hôpital's Rule when it is convenient and applicable.   lim x→∞…

A: The given limit,      limx→∞1+axx, for some constant 'a'

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A: The objective of the question is determine the length of the given curve.

Q: Find a formula for the general term an of the sequence, assuming that the pattern of the first few…

A: Topic = Series

Q: 2 For the f(x)=2x² - 4x² defined -2≤x≤3 on the interval A. Find all critical points B. Find absolute…

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Q: dz 10. Evaluate the integral where C is a simple closed curve cz(z - 1)' in the positive direction…

A: The integral ∫Cdzzz-1, where C is the simple closed curve in the positive directionthat contains the…

Q: Use Green's Theorem to Calculate the Line Integral ſy²dx + x²dy, where c is the triangle o vertices…

A: Given that, the line integral is ∫y2dx+x2dy and the vertices of the triangle is 0,0,4,0 and 4,4. By…

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Q: The differential equation 2ydx-(3y-2x)dy=0 is Exact homogenous and linear O

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Q: Why are 9x^2-81y^2=0 and 9x^2-(z^2/4)=0 hyperbolas that pass through the origin and not lines that…

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Q: The definite integral is equal to O 2 [²x Select one: 4 O f₁²₁x² dx + ₁ + x² dx none of the others ○…

A: ∫02 x2dx here we have to find equal to this. split the integral into two  use formula  ∫a  b f(x)dx…

Q: Write the given expression as an algebraic expression in x. sin(2 tan-¹(x)) X

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Q: Find the indefinite integral. (Use c for the constant of integration.) [ (42³1 + (4t³i + 14tj…

A: We need to find integral.