Verify that the line r(t) = [1 + t, 1 - t, t] is part of the one sheeted hyperboloid x^2 + y^2 - 2z^2 = 2.

Q: dz Evaluate: ¹5 10+2x 01 O Divergent O 0 O-1 15

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A: The required partial derivative is evaluated below.

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Q: Find the general solution of the following differential equation. y” + 5y′ − 14y = 0 NOTE: Use c₁…

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Q: ) Consider a horizontal parabola of the form ay² +by+ c = x wherea #0 and whose graph contains the…

A: Given problem:- Consider a horizontal parabola of the form ay² +by+ c = x whose graph contains the…

Q: 1. (xy² - x²) dx + (3x²y² + x²y - 2x³ + y²)dy = 0

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A: Side of cube is increased from 5 to 5.2

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Q: Evaluate S ○ In O Divergent ○ In 11 O 6 In 11 6 dz 2²-25 16

A: Given problem :- ∫6∞6x2-25dx

Q: Find the gradient of the function at the given point. Function Point (3, 7, 2) f(x, y, z)=√√√√x² +…

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Q: Question a) b) Let f(x, y) = 2√x - y²e-²xy + ²². Find fx and fy. Evaluate fxxy(4,-1).

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Q: Question 11 Find dy/dx of y = log₂ (x log5 x) In a alna ln 2 O y =

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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: Let Find fy. f(x, y) = x²y + √√x + 5y

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Q: and x = = z = e-22 In (2-y), Select one: O True O False - 6t, y = t-s, then the value of 3 is equal…

A: In this question we have to find whether the given statement is True of False.z=e-2x…

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: O ди If u = f(x,y), x = g(w) and y = h(w), using Chain Rule, what is aw O ди aw ди Əw || O all of…

A: u=fx,y, x=gw and y=hw

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: Find the domain of f(x, y) = Vy+I y(1-x²)

A: Given: f(x,y)=y+1y1−x2 The domain of functions of two variables, f(x,y) are regions from two…

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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: Consider the function f(x)=5/x^2 - 9/x^7 Let F(x) be the antiderivative of f(x)with F(1)=0 then…

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Q: of If then fry(0, 1) =? Select one: O 1 f(x, y) - O None of them - sin y x cos y,

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Q: The solution of the following non exact differential equation (cos x) dx + (1+² sin x)dy = 0 is:…

A: The given differential equation is;  Cosx dx +(1+2/y Sinx) dy=0

Q: graph 10 5 0 answer 5

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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: 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: A solid figure projects the same shape on the x-y, y-z, and x-z view. Which of the following…

A: Note that the sphere will projects circles on the xy, yz and xz view.

Q: 3. For y = 3 sin x + 21, the third order derivative (a) -3 cos z +21 (b) -3 cos r 4. For y = e-2-50,…

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Q: Which of the following is the answer of x² - y² ·? lim (x,y) (5,5) 2x - 2y Select one: -5 O 5/2 05 O…

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

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Q: Choose the correct answer for the following limit: Select one: Ο Α. 0 O B. Does not exist. OC. None…

A: According to question,Given Limit,Let l = limx, y→0, 0x3 + 6y25x3 + y2

Q: Find the solution of the given initial value problem. y(4) 10y""+25y" = 0; y(1) = 10 +e5, y'(1) =…

A: This is a problem related to differential equation. Please follow the procedure given below.

Q: If f(x, y) = x²y + cos(x) then (fx, fy) = (2xy + sinx, x²). Select one: O True O False

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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: 1. Find the domain of the vector function r(t) =

A: 1. Given Vector Function,rt = lnt+2, t1-t2, 2tt2 -4

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: ات, 01 +19+₂1 x+₂²0 +19+₂. 1. Evaluate

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Q: Evaluate: ffefdxdydz 0-1/1 O 01/12 O-1 S

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Q: No 1 2 3 Problem Use the method of disks/rings to determine the volume of the solid obtained by…

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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.

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Q: Given the graph of f, find any values of x at which f' is not defined. A 44 SOU OA. x= -1, 0, 1 OB.…

A: Solve the following

Q: Which of the following is the gradient vector of the function f(x, y, z) = cos ry sin yz? Select…

A: Here, the given function is: f(x,y,z)=cos(xy) sin(yz) Note that the gradient vector is given by:…

Q: No 1 Problem Use the method of disks/rings to determine the volume of the solid obtained by rotating…

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Q: if a = (3, 2, 9) and b = (-4, 7, 2), find a • b.   a) a • b =-9   b)  a • b = 19   c)  a • b =…

A: In this question we have to find the value of a·b

Q: Use an appropriate test to determine whether the series converges. k² +3 2 k + 3k +2 2k²+1 Σ k=1

A: The given series,        ∑k=1∞k2+3k+22k2+1

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

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