12. If eie + 1 = 0, what is 0? A. 0 B. π 2 C. T D. 2π E none of the above

Q: 3. (x² + y²)dx - 2xydy = 0 [Answer: x²-y² = cx]

A: Here we use the method of substitution y=vx then dydx=v+xdvdxsee below the calculation and…

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: What is the integral of f cos¹ (2t)dt? Ot+sin(4t) + sin(8t)] + C O None of the choices O cos¹ (2x)…

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Q: circle is inside a square. The radius of the circle is decreasing at a rate of 3 meters per hour…

A: Here we have to use the concept of derivatives

Q: Find concave upward and concave downward of 6x^2-x^3

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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: (x³ − 2y²)dx + 2xydy = 0 -

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Q: 1. The two graphs below (X & Y) show two functions from our library of common functions. For each…

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Q: Given the matrices A - 5 -5 2 2 2 - 2 and B - 4 2 -1 -2 5 0 A. It is Select an answer to multiply…

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Q: Find lim PHEL x² + 100-10

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Q: Estimate the area under the graph of f(x)=1/x+2 over the interval [2,5] using eight approximating…

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Q: If A(3, 2, 9) and B(-4, 7, 2) are two points in 3-space, then find the vector AB. a)  AB= (-7, 5,…

A: If A(3, 2, 9) and B(-4, 7, 2) are two points in 3-space, then find the vector AB.

Q: A heart-shaped graph in a 2D plane is defined by the equation (x² + y² - 1)³ = 4x²y³ Determine dy/dx…

A: See this solution in below

Q: 2. Find the area of the region enclosed by the parabola y = 2 - x² and the line y = -X.

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Q: Which of the following is a valid expression for cos ¹ x? 04-sin-¹ a 01/2+ + sec¹ a 1 sec-1 01-…

A: The given expression is cos-1(x)We have to find the valid expression for cos-1(x)

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

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Q: √x +3 If f(x, y) = xy +7 the domain of f(x, y). Select one: True O False then the point (1, −7) is…

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Q: The following limit lim Select one: 16 equals 1 3 equals 0. does not exist. None of them equals 2x²…

A: To evaluate the following limit.limx,y→-2,2 2x4+2y43x2-3y2

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

A: This question can be solved using the concept of horizontal and vertical asymptote of rational…

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

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Q: Evaluate (x² - 1)³² dr.

A: Our Aim is to evaluate the integral given below:-∫x2-12 dx -(i)

Q: Find (²-1) ln(x)dx

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Q: Let Z=ellxy-56y and x = 56t6 + 6 and y =sin(s + 56). Use the dz дz Chain rule to find and Ət - ds

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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: In(t³ + 1) + t³ + 1 r(t) = 4: then the limit lim r(t) equals 1-0 -i-(4e-²¹-5e²¹)j- - sin³t -k, 13

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Q: Solve the given dy=x√ e+~

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

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Q: r(t) = (−2√√ť² – 4, 3 sin (4t), 3 ln (−5 – 2t)), then the domain of r is given by the interval…

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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: 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: The annual number of passengers going through Hartsfield-Jackson Atlanta International Airport…

A:

Q: = 2√/16 - x² - y2, then the domain of D = {(x, y) x² + y² ≤ 16}. 2

A: We have to choose the correct option from the given options according to the given information

Q: 9 Evaluate f 99√x 30-x2 -x² 2 dx.

A: ∫4999x30-x322dx

Q: Work Problem for the question. Let You must provide a clear and detailed solution z = (y-2x)³. where…

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Q: x - 4y = 26²

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Q: Evaluate: S 2y+3 (y-1)(³-1) dy ○ − In\y − 1| − § (y − 1)³ + ½ In|y² + y +1| - arctan (√3(2y+1) ) +…

A: To evaluate: I=∫2y+3(y-1)(y3-1)dy=∫2y+3(y-1)(y-1)(y2+y+1)dy=∫2y+3(y-1)2(y2+y+1)dy

Q: Evaluate fz² In z dz using integration by parts O² Inz-+c Onz-+c Onz-+c 2²lnz - 2 + c 12 21

A: Solution:  step-1: Evaluate ∫z2*lnz dz using integration by parts                Formula for…

Q: Question a) b Let f(x, y) = x³-4xy² x²-2y Find the first partial derivatives of f. Determine whether…

A: According to question,Given Function,fx, y = x5 -4xy2x2 - 2y

Q: is

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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: Find the minimum rate of change at (2,-2,0) and it's direction for f(x, y, z)= =. zy² H in the…

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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: ax+2, x≤2 f(x)=4-x². 2<x<3 2x+b. 3 < x Find the value of a so that f(x) is continuous at 2. Find the…

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Q: Suppose that the yield (measured in kg/ ha) of an agricultural crop is represented by the function…

A: We need to find rate.

Q: 01. |x2 - 1\dx = a. b. 2 C. 432 - 23 23 d. 틀-

A: This question can be solved using the concept of definite integrals and modulus function.

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

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Q: Evaluate foxe*² dx . 2 0 a. b. OC. O d. 9 =/12 + C 2 2 (e⁹-e) + C (e⁹-1) + C (eº-x²) + C

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Q: A 4 C 5 3 Find sin(ZABC +60°). B

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

A: Given :fx,y=2x-y2e-2xy+2y