Find the volume of the solid generated by revolving about the line x = -4 the region bounded by the two parabolas x = y - y^2and x = y^2 – 3

Q: Let z = (y - 2x) ³, where x = s′ s²t and y = st². Use the Chain Rule to dz find when s = 2 and t =…

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Q: Find the limit, if it exists, or show that the limit does not exist. 2 x² - 3y² lim (x,y)→(0,0) x² +…

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Q: Use the Divergence Test to determine whether the following series diverges or state that the test is…

A: This question can be solved using the concept of divergence test.

Q: if z=xarctan(y/z), find ∂z/∂x at x=0, y=1, z=1

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Q: with

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Q: Let the function f(x) have the property that f'(x) = ¹.1f g(x) = f(x²) find g'(x). g'(x) = Solution:

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Q: Use the given information to find the exact value of the trigonometric function.  sin θ = 1/4 , tan…

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Q: A 4 C 5 3 Find sin(ZABC +60°). B

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Q: The domain of the function f(x, y) = Inz x-y is: Select one: O The region below the line y = x but…

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Q: lim cot 1 -1 8418 1

A: A detailed solution is given below.

Q: find the rate of change of the circumference of a circle when the area is increasing at the rate of…

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Q: Integrate: S (2x2-10x+15) gở ba tô 2x + 3 ln() + C ○ 3 ln()+ +C O 2x+3 ln()+ ○ 3 ln() + C +C dx

A: ∫(2x2-10x+15)x2-5x+6dx=∫(2x2-10x+12+3)x2-5x+6dx ∫2(x2-5x+6)(x2-5x+6)dx+∫3(x2-5x+6)dx…

Q: Find the minimum distance from the point (5, 0, 0) to the paraboloid z = x2 + y2. (Give your answer…

A: To find the minimum distance from a point to a paraboloid is just to minimize the function…

Q: Find dy/dx by implicit differentiation and evaluate the derivative at the given point. dy dx At 4, x…

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Q: If z = √√√xy, dz and x = t², y = 1² then =? dt Select one: O √xy(21) O √xy(21²) 0 2t O None of them…

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Q: Question 1 Let C be a curve defined by the vector equation r(t)= <8t³ - 9t, 8t³ +7t, e8³-917. Show…

A: Solve the following

Q: The limit exists and is equal to 0. Select one: O True O False lim (x,y) →(0,0) 36x²+25y² 6x+5y

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Q: 1. Find the domain of the vector function r(t) =< ln(t + 2), t 1 - 12 21 √12 - 4

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Q: Evaluate f 2x³ +9x (x²+3)(x²-2x+3) dx

A: Evaluate ∫2x3+9xx2+3x2-2x+3dx=?

Q: Find the directional derivative of the function at P in the direction of v. f(x, y) = x³y³, P(8, 3),…

A: Here we have to find the direction derivative.

Q: Evaluate: cot¹ (+) -do 0² O None of the choices Ocot³ (1)-cot (1) + 0 n ( ² ) − ² + c - ()επει ο -…

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Q: If f(x, y) = A In (x² - y) -x+y+1 O {(x, y) x² > y, {(x,y)|x² ≥ y, ○ ○ {(x, y) x² > y, | then the…

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Q: The domain of f(r. y) = Select one True False 19-y V is the upper half of the disc centered at…

A: fx,y=9-x2-y2y

Q: Let f(x) = X x - 3 g(f(x)) = and g(x) = 4 X Find the following functions. Simplify your answers.…

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Q: A y=1 x=y² B y=x² C (1, 1) X=1 X (0,0) Region A is bounded by the parabola x = y², the line y = 1,…

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Q: z = (x + y)², x = s²t, y = st². Use the Chain rule to find dz ds for t= 1 and s = 2.

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Q: Find all relative extrema. Use the Second Derivative Test where applicable. (If an answer does not…

A: Suppose that x=c is a critical point of fx then, If f 'x&gt;0 to the left of x=c and f 'x&lt;0 to…

Q: A screen saver displays 3 cm x 5 cm and then expands it in such a way that the length of the longer…

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Q: area bounded by a = √y, x = 0, and y = 3 with the axis of revolution at y-axis using horizontal…

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Q: Use the formula for the sum of the first n terms of a geometric sequence to solve. Find the sum of…

A: Sum of first n terms of a geometric sequence is given by Sn=arn-1r-1 where a is te first term and…

Q: Find the limit, if it exists. x² lim X-5 000 A. B. - 2x - 15 X +3 -8 5 C. 0 D. The limit does not…

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Q: Work problem 3 ( Given the vector function F(t) = (6t³ - )) 5 sec(4 — t)), then find the tangent…

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Q: For the following telescoping series, find a formula for the nth term of the sequence of partial…

A: Here we have to find the limits and then state whether it diverges or not.

Q: Use the formula for the general term (the nth term) of a geometric sequence to find the indicated…

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Q: Question 35 If z = x arctan 0 - 4 OFF O undefined ◄ Previous (²).find əz əx at x = 0, y = 1, z = 1.

A: To find the partial derivative of z with respect to x.

Q: Evaluate cosh² x dx }(sinh2n +2) + 0 +x + C O2e²x +4z + C 8 O None of the choices cosh(z)sinh(2)++C

A: We can solve this as follows:

Q: If then fxx = Select one: True False 2(y² + y) (y - x)³ f(x, y) = x + y² y-x

A: According to question,Given Function,fx, x = x + y2 y-x

Q: Consider the infinite series > Evaluate the first four terms of the sequence of partial sums. k=1…

A: Given that infinite series       ∑k=1∞1k+3       We have to evaluate first four terms of the…

Q: Question af If f(x, y) = xy² - x ln(y) find Ət if x(t, s) = s² - st³ and y(t, s) = e-st².

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Q: an upright cylinder with a base radius of 5cm and a height of 10cm has a possible error of 0.08cm…

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Q: Assume mmh (x) = f(g(x)) such that the first an exist g Second derivatives of both of and What is b"…

A: Assume h(x) = f(g(x)) such that the first and second derivatives of both f and g exist  We have to…

Q: Find the first partial (a) derivatives of the function f(x, y) = x²y√√y + 4y². (b) fxyx of the…

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Q: Find a set of parametric equations of a circle centered at (2,3) with a radius 2 generated clockwise

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Q: A polynomial f(x) and one or more of its zeros are given. f(x)=x²-4x³+27x² +8x-58 2-5i is a zero…

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Q: Evaluate the integrals using partial fraction 3y²-y+! S y³ - y² dy

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Q: The differential equation Find such a solution and then give the related functions requested. dy =…

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Q: 1. Find the gradient of the function f(x, y, z) = ln(xy) - zx² at the point (1, 1,-1).

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Q: If y = xcosx, what is dy if x = and dx = 0.2 ? 0-1/2 0-20 05/0 O EN T 10

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Q: 1. Find the gradient of the function f(x, y, z) = ln(xy) - zx² at the point (1, 1, -1). 2. Find the…

A: Given :fx,y,z=lnxy-zx2

Q: Find the interest earned on $30,000 deposited into an account paying 2.5%. Round to the nearest…

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