8x³ - y³ 3 lim (z,y) (1,2) 2x - y Select one: O equals 12. O equals 0. O None of them O equals 4. O does not exist.

Q: If f(x) is a differentiable function then f'(a) is given by which of the following? f(x) = f(a) I.…

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Q: None of the other choices 7 The curve y = f(x) has the horizontal asymptote y = Select one: 00 1…

A: Given function:- f(x) = (x+35)/(x-5)  To find:- Horizontal asymptote of f(x)

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: 14. Show that the demand function D(p) =alp', where a and b are positive real numbers, has a…

A: Solution is given below:

Q: Given that the graph of f(x)f(x) passes through the point (5,10)(5,10) and that the slope of its…

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Q: Use MUPAD to determine the following indefinite integrals (7.1) (7.2) (2ax-x²)³ dx. S (7.3) Obtain a…

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Q: The matrix The larger eigenvalue A-0 has multiplicity 1 0 has two real eigenvalues A, < A. Find…

A: The eigenvalues of A are the roots of the characteristic equation detA-λ I=0 So,…

Q: Question 1 function r(t) = (tª In 1, ¹2³, −3e¯³¹). a) Find the integral r(t)dt. b) Find parametric…

A: Here, r(t)=t4ln t, t-32,-3e-3t

Q: Given y = cos(3x), find O O 3 2- * N O √3 3√3 dy at x = 5

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Q: Find a set of parametric equations of the line segment from (-1,-3) to (6,-16)

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Q: given z=xlny-((2^x)/y)+ysinhsqrtx, find (∂^4)z/∂x∂y∂x∂y

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Q: a) b) exist f(x, y) = x²yesy 8x²+7y² Find the domain of the function f. Show that lim f(x, y) does…

A: According to question,Given Function,fx, y = x2 y e5y8x4 + 7y2

Q: Question 40 The graph of y=2 is concave downward for all values of such that. 0 x 2 0x 0 < Previous

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Q: 15 0 2) is an eigenvector of the matrix 25 -12 -6 A = 60 -31 -15 -36 22 10 associated with the…

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Q: Question 12 Find the 2nd derivative (y") of y=√x ln x In 2

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Q: 4. (xy² + 2x²y³) dx + (x²y - x³y²) dy = 0

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Q: Let z = √√√7xy +9y, and x = s³ and y = 1². Use Chain Rule to find dz when t = 1 and s = 2. ds

A: To find out the given partial derivative.

Q: Explain why the vectors u₁ = (2, 4,-4) U₂ = (-4,-8, 8) form a linearly dependent set of vectors in…

A: To find the reason for the given vectors to be linearly dependent.

Q: Determine the derivative of the following function and simplify: tan³ (22) sin² (5x) - O 2 tan² (2x)…

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Q: Find the limit of the following sequence or determine that the sequence diverges. {tan - 1 (₁ -1…

A: Here we have to find the limit of a sequence.

Q: Find the arc length of the following curve on the given interval. x= 12t³, y=18t², 0sts √3 The arc…

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Q: Question 1 [ Let 7 f(x, y) =ln(xy)-50x³y Find fx, fxy and fxyx.

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Q: Numerically estimate the slope of the line tangent to the graph of the function f at the given input…

A: Given function :- f(x) =3√x  Estimate f'(1)

Q: (z In z + 5)dz

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Q: A bush fire is burning a circular area whose radius is increasing at a rate of 3 ft/min. How fast is…

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Q: Use the graph of m(x) shown to answer the questions below. -5 10 50 0 5 a. State the domain of m(x)…

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Q: e the figure to answer the questions. point A point B B point C point D point E y C D (a) At each…

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Q: What is the angle of inclination? x +₂y + 8 = 8=0

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Q: 2x² sin x + 3y³ 3x³ + 2y² lim (x,y)→(0,0) if we approach along y-axis, we will get Select one: True…

A: This question is based on two variable limits.

Q: EV None of the choices Ocot³ (1)-cot (1) - ○tan³ () - tan() Ocot³ (¹)-tan (1)

A: givenI=∫cot4(1θ)θ2dθlet  1θ=x-1θ2=dxdθ1θ2dθ=-dxI=-∫cot4(x)dx…

Q: b) Evaluate lim X-8 In(5x) In(2x-4)

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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: Choose the correct answer for the following function: f(x, y) = cos(2x²y³) Select one: None of the…

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Q: Find the horizontal asymptote(s), if any, of the curve f(x) = (x-x+) -16 Select one: Ⓒ x = 4, x=-4 O…

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Q: Use Newton's method to find the absolute maximum value of the function f(x) = 5x cos(x),    0 ≤ x ≤…

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Q: Let z = √√√7xy +9y, and x = s³ and y = 1². Use Chain Rule to find dz when t = 1 and s = 2. ds

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Q: f(x, y) = 6√x - y²e-³xy е a) b) + elw Find få and fy. Evaluate frzy (4, −1).

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Q: A dam has a semi-circular gate at the bottom that is 4 m in diameter. The dam is 12 m high and…

A: Given data as follows :- Diameter of the semicircular gate is 4m. Height of the dam is 12 m.  Water…

Q: A road perpendicular to a highway leads to a farmhouse located a = 1.5 km away. An automobile…

A: This question is based on application of derivative.

Q: A man of height 1.9 meters walks away from a 5-meter lamppost at a speed of 1.1 m/s. Find the rate…

A: topic- application of derivatives

Q: lim cot 1 -1 8418 1

A: A detailed solution is given below.

Q: Find a normal vector to the level curve f(x, y) = c at P. X = x² + y² P(5, 5) f(x, y) = C = 100

A: To find the normal vector.

Q: A movie theater has a seating capacity of 163. The theater charges $5.00 for children, $7.00 for…

A: A detailed solution is given below

Q: Does the sequence {an} converge or diverge? Find the limit if the sequence is convergent. an = tan…

A: The given sequence,   an=tan-1n

Q: Evaluate: St dz 2√√7+3 ○1-3 ln(7/5) O 2-3 ln(7/5) 2 2+3 ln 7 03-In()

A: Given :∫14dx2x+3

Q: QB3) Verify fxy-fyx for the function f (x, y) = 4x (Iny) + 4y (Inx) + (²²4 2²

A: We have to prove fxy=fyx for the given function.

Q: 3. You are in a boat 2 miles from the nearest point on the coast. You are to go to point 2. → down…

A: Note: As per our company guidelines we are supposed to answer the first three sub-parts of the…

Q: What is the equation of the tangent live the When X = 4 √(x) = ² -6√x cheve f(x) = 3/

A: Given ::fx=8x-6xx=4

Q: Find an equation of the tangent plane to the surface at the given point. x² + y²5z² = 29, (-3, -5,…

A: Solution of given question is written in below steps.

Q: Consider the function f(x)=5x2−9x7f Let F(x)F be the antiderivative of f(x)with F(1)=0 then f(x)

A: we have to find the function F(x) .