Find the gradient of the function at the given point. w = x tan(y + z), (7, 15,-5) Vw(7, 15,-5) = tan 10i+ 7 sec²10j + 7 sec²10k X

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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: Find the general solution of the following differential equation. y" + 4y + 8y = 0 NOTE: Use cy and…

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Q: If f(x, y) = 2√√x² + y2 - 16, then the domain of f is the set D = {(x, y) x² + y² ≤ 16}. Select one:…

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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: Evaluate f cosh² x dx đ (sinh 2 từ t + x) + C O 2r O2e² +42 + C 8 O None of the choices…

A: We have to evaluate  ∫ cosh2(x) dx

Q: What is the integral of f sin² x cos²x dx? O cos(z) sin³ (2) cos(z) sin(z) + 4 4 O sin(4x)+4z 32 +C…

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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: 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: 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: 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…

A: Lim(x, y) -(1,2)(8x3-y3)/(2x-y).

Q: Use the limit definition of partial derivatives to find fx(x, y) and fy(x, y). f(x, y) = x2 − 5xy +…

A: We need to find partial derivative.

Q: 2 2 If z = f(x, y), where x = s² - t² and y = t² s² and z is differentiable, then - Select one: True…

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Q: Evaluate fz² In z dz using integration by parts Oz² Inz-+c Oz-+c Onz-+c Oz²lnz-/+c 12 2₁

A: A detailed solution is given below

Q: (2x²-10x+15) 22 50 tôi 2x+31(2-3) + G Integrate: f -dx

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Q: Evaluate: 12+3 2√x+3 ○1-3 ln (7/5) O2-3 ln(7/5) 2 O2+3 ln7 03-In()

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Q: A B O A OB O OD 1 13 (sin(3z))¹⁰ + C 1 33 ſ cos(3z)sin¹⁰(3z) dz 1 3 (cos (3z))¹¹ + C F None of the…

A: Here we have to find the integral.

Q: 2x² + 5x-1 x³ + x² 3 -dx x² – 2x

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Q: (x, y) 5) 4x2+2y2 Find the domain of f. Show that the limit does not exist. lim f(x,y) (x,y) → (0,0)

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Q: (x¹+y¹) dx - xy³ dy = 0 [Answer: y = 4x¹logx + Cx¹]

A: This question is based on Homogeneous differential equation.

Q: Sketch the graph of y=x+4 and give the exact coordinates for both the x-intercept and the…

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

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Q: For the curve f(x) = Find the horizontal and vertical asymptotes. x-4x² +2 x² - 4x +4

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Q: Question a) b) 2xy Consider the function f(x, y) = 4x²+5²- Find the domain of f. Show that the limit…

A: To find out the domain

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Q: If f(x, y) = Select one: O None of them In (x² - y) then the domain D of the function f is given by…

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Q: If f(x, y) = 9x² - 6y³ - 7 cos(-6xy + 플) then Select one: O True O False fy(л,0) = -42

A: Given function is f(x,y)=9x2-6y3-7cos-6xy+π2. We have to find fy(π,0) that is partial derivative of…

Q: Evaluate fz² In z dz using integration by parts Oz²lnz-+c Oz-+ +c Onz-+ C Oz² Inz-+c 2₁

A: Given: ∫z2lnzdz

Q: Suppose that the concentration (measured in gm3) of nitrogen in the soil along a transect of land…

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Q: Find the general solution of the differential equation. y"" — 17y" +82y' — 120y = 0. NOTE: Use C₁,…

A: Here we have to solve the differential equation.

Q: lim cot 1 -1 8418 1

A: A detailed solution is given below.

Q: 1. (x³y³ + x²y² + xy + 1)ydx + (x³y³ – x²y² - xy + 1)x dy = 0

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Q: 3) [A Consider the DE: -(4x³y - 16)dy = (6x²y² – 10)dx. A) Show that the differential equation is…

A: Use exact equation

Q: The partial derivative of the function f(x, y) = 4x² – 3xy + 5y-e³+8y with respect to x is: Select…

A: To find out the partial derivative of the equation.

Q: 12. Show that the general linear demand function D(p) = a - bp, where a and b are positive real…

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Q: Can you please show the working i do not understand.

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Q: P₁: -60x + 90y + 120z = 29 P₂: 4x - 6y - 8z = 5 P3: -20x + 30y + 40z = 4 P4: 12x18y + 24z = 9

A: Follow the procedure given below.

Q: If f(x, y) = 2√/16 - x² - y², then the domain of f is the set D = {(x,y)|x² + y² ≤ 16}. Select one:…

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

A: Evaluate ∫2x3+9xx2+3x2-2x+3dx=?

Q: Question a) b) 2xy Consider the function f(x, y) = 4x²+5y² Find the domain of f. Show that the limit…

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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: Which is not the about f(x) = |x|? Continuow at O no targent line at 0 Derivative from left at O is…

A: Use the function value to evaluate which one is false

Q: z = e Select one: True False In (2-y), dz and x = s² - 6t, y = t - s, then the value of when t = 4…

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

A: We need to evaluate integral.

Q: 4. Evaluate (²52³Vl-Pax

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Q: Work problem 3 Given the vector function F(1) = (51³ — —, sec —7, sec(3 − 1)) - then find the…

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Q: x³ - 2x + 3 lim x++∞ 64x² – 3x³

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Q: Let A = A(r) give the area of a circle of radius r. The instantaneous rate of change of the area as…

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Q: f(x, y) = 6√√√x – y²e- - a) b) y²e-3ry + | co y Find f and fy. Evaluate fazy (4,-1).

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