Find the area of the region bounded by the curve y=x²-1 and the line y = 24! The area is

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: Identify the open intervals on which the function is increasing or decreasing. (Enter your answers…

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Q: Find lim PHEL x² + 100-10

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Q: Jo 1 X dx =

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Q: Question 22 A square is increasing in area at a rate of 20 mm² each second. Calculate the rate of…

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Q: If then fyy = Select one: O True O False f(x, y) = 2(x² + x) (x - y)³ x² + y x - y

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Q: The limit lim (x,y)→(4,-5) exists and equals to Select one: O True O False 25x²-16y² -5x-4y -40

A: Given the limit is  limx, y→4,-5 25x2-16y2-5x-4y.

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: If y = x?, then dy = a Ο 2 Δε Ο 2 Δy Ο 2 Δε Ο π*Δy

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Q: Question 24 Which of the following statements is true about critical points? O It is a point in the…

A: We have to choose correct option for given question.

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

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

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

A: Use exact equation

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: 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: is

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Q: 4. Evaluate (²52³Vl-Pax

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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: Let f(x) = x³ + √√. Then f'(1) = 02 O 1.5 O 3.5 04

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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: Find the smallest number of terms of the series Σ1 partial sum sn is within of the sum. 1 100…

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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…

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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: A square is increasing in area at a rate of 20 mm² each second. Calculate the rate of change of each…

A: topic- application of derivatives

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

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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: √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: 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: Evaluate the limit: limo* [cos(3x)]= O e-3 03 e 01 ◄ Previous

A: To evaluate the limit.

Q: Which of the following are the tangent lines perpendicular to y = x, to the curve x + y² = 8? Oy=x+8…

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Q: Region A is bounded by the parabola x = y², the line y = 1, and the y-axis. Region B is bounded by…

A: As per the instruction, we will be answering the first question. Given: We need to find the volume…

Q: Explain (in words) what transformations it takes to transform the function f(x) = x³ into the…

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Q: If f(x, y) = In (x² - y) -x + y + 1 then the domain D of the function f is given by the set

A: Given :fx,y=lnx2-y-x+y+1

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

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Q: 9 -8 -7 y=x+2- 3 4 5 7 8 9 10 Find the average value of f(x) = x + 2 on the interval [1,4]. Hint:…

A: The average value of fx=x+2 on the interval 1,4

Q: A 4 C 5 3 Find sin(ZABC +60°). B

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Q: 1 Give the antiderivatives of X The antiderivatives of 1 2 are

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Q: If and x = 2t, y = 5t, then the value of equal to 12. z = x - 2y, Select one: O True O False dz dt…

A: Given that , z=x-2y and x=2t , y=5t find dzdt at t=3.

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

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