Suppose 4x2 + 16y2 = 100, where x and y are functions of t. dy (а) If dt 1 dx find when x = 3 and y = 2. dt dx dt dx (b) If dt dy when x = -3 and y = 2. dt 4, find dt II

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A: Given,            fx=43x2-2x+13To find : f'-1

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A: We will find the implicit differentiation. 

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Q: If f(x) = 7 cot-l+ 5, then find the value of f'(-6) is -5 37 -6 37 O 00 O 7 37 O -7 37

A: Topic:- application of derivatives

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A: We can answer all parts as below.

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A: ∫∫D f(x,y) dx dy = ∫y1y2∫x1x2 f(x,y) dx dy

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Q: 11 Find the area of the region bounded by y = x² + 2x – 1, y = + x x = -3, x = 1. 2

A: Area between curves

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A: We can rewrite the integral using substitution as below.

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A: We can find the volume as below

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Q: sin(4-y)sin(3-y)dy

A: Use the formula sin(A) sin(B)=12(cos(A-B)-cos(A+B))Consider ∫sin(4-y)sin(3-y)dy=∫12(cos(4-y-3+y)-cos...

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Q: find the approyimate Valueof 10/3 2- |(3.01*+(5-98)²+(2.03)?

A: According to guideline I'm solving only Question no. 2 

Q: dder the folowing. TX) - V 30 - tch the graph of the function. Use a praphing utlty to vertfy your g...

A: Given query is graph the function and find domain and range.

Q: dx (apply the properties on how to solve improper integrals 1 – x²

A: Given query is to find the value of the integral.

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A: For finding eigenvalues of Matrix A , find A-λI =0.

Q: Find the acceleration of the potato at 0.5 s ft/s?

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Q: The solution of the given equation (1+x²) y' + 2xy = 4x² is: O y=[(4x^3)/(3(1+x^2))]+C(1+x^2) O y=[(...

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Q: Question 8 TT Evaluate: " sin7 Cos4 dx

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Q: 1 dx (2x + 1)4

A: We will use concept of improper integral here. 

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A: Given query is to find the differential.

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Q: V3 7. arctan 3.

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Q: Find the relative extreme of the function f (x) 12+2x+2 and where they occur.

A: Given: - The function is, f(x)=x+1x2+2x+2 To find: - The relative extreme of the given function.

Q: Find the centroid (, j) of the region bounded by: . y = 3x + 8x, y = 0, x = 0, and x = 6 %3D y =

A: The given problem is solved below in detail.

Q: 34x + 16 f(z) g(z) The partial fraction decomposition of 8x2 can be written in the form of - 14x + 3...

A:

Q: dy Find using implicit differentiation, for the equation a + = 11 is. da

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Q: bx a a dy dx 0. 0,

A: The value of the given double integration is ab/2

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Q: az az Find and e = 5x 2² + sin(r + 2) – y?.

A: Find the partial derivative of z with respect to x and with respect to y respectively

Q: 6 The coefficient of sin( 2x) in the antiderivative of F(x) = cos is Blank 1 (use fraction form not ...

A: ∫cos6(x2)dxsubstitute u=x2→dudx=12→dx=2du=2∫cos6u du=2[cos5u.sinu6+56∫cos4u du]=2[cos5u.sinu6+56[cos...

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