A B - f sin(1-x) (2 cos(1-x))4 dx (2-sin(1-x)5+C 5 (2-cos(1-x)5+C 5 O A OB O O D OE None of the Above C D (2-sin(1-x)5 5 +C (2-cos(1-x)5 5 + C

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…

A: To find out the value of a as f(x) is continuous at 2.

Q: lim t→∞ 14/3 + 71/3 2 (6+²/3 +11) ²

A: To find out the limit.

Q: A y=1 x=y² B y=x² C (1, 1) X=1 X (0,0) Region A is bounded by the parabola x = y², the line y = 1,…

A:

Q: find the rate of change of the circumference of a circle when the area is increasing at the rate of…

A:

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: 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: Find (²-1) ln(x)dx

A:

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: Evaluate: 0 tan-¹ (0) de Ô arctan(9)–0 2 arctang+ -arctan0+C 0—arctan(0) +C

A:

Q: Question a) b) Let f(x, y) = 2√x - y²e-²xy + ²/3. Find fx and fy. Evaluate fxxy(4, -1).

A: Given: For (a),     ∂ ∂ x2x-y2e-2xy+2y=∂ ∂ x2x-∂ ∂ xy2e-2xy+∂ ∂ x2y=1x--2y3e-2yx+0=2e-2xyy3+1x    ∂…

Q: The integral 2 fossin drde is equal to π/2 O-1/2 O 1/2 0 1 00 10

A:

Q: $] A) Solve the IVP: 2) [23 (2x - 4). - 2 ln 5x + 2y = 0, y(3) = 3. dy dx B) Give the largest…

A: Concept: Initial value problem (IVP): Initial value problem (IVP) or Cauchy problem is the term used…

Q: Given the functions f(x, y) = 4 cos(4x - 6y) and g(x, y) = -6 cos(4x - 6y). af The partial…

A: Here we have to use the concept of partial derivatives

Q: Apply Newton's Method to f(x) and initial guess xo to calculate x₁, x2, x3. f(x) = x² - 6x + 4, xo =…

A: We have to find the x1, x2 , x3.

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

A: Given problem :- ∫6∞6x2-25dx

Q: 2n Consider the series ₁ (-1)" (1 + 1)². Which of the following statements is true? n=1 The series…

A: A series ∑n=1∞ an is said to Converge Absolutely if the series ∑n=1∞ an converge and Conditionally…

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

A:

Q: Solve this system of equations x2+2y=0 -y2+2x=0

A:

Q: 1= z In zdz

A: Given, ∫ xlnxdx

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

A: To determine whether the following statement is True or False.limx, y→0, 0 2x2 sin x+3y33x3+2y2if we…

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:

Q: Given f(x) (x + 21 -x² 4 x < -1 -1 < x < 2 x ≥ 2 a. Evaluate f(-3) b. Evaluate f(-1) c. Evaluate…

A: We need to find values of function.

Q: If f'(1) = 4, f(1) = 2, and g(x) = f(x) tan-¹x, what is the slope of the tangent line to the curve y…

A: Here we have to find the slope of the tangent line.

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

A:

Q: Let f(x) = 2x+1, if x1 O (-∞, 1) U (1,00) O (-∞0, 1] U (1, ∞0) OR O (-∞0, 1) U [1,00)

A: topic- limits and continuity

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: Use Cauchy's Integral Formula and Cauchy's Integral Formula for Derivatives, when appropriate, to…

A: See this solution in below

Q: Find the limit lim 3-0 Select one: 04/3 None of these Does not exist -8/6 00 8x² + 7x-9 6x²-2 if it…

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

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Q: Find the points of inflection of the graph of the function. (If an answer does not exist, enter…

A:

Q: (2x²-10a+15) da Integrate: f gở ba tô 2x+3 ln()+ +C n(²²³)+c +C 3 In O2a +3 ln()+ ○ 3 ln() + C o +C

A: We have to integrate ∫2x2-10x+15x2-5x+6 dx.

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: Where is f(x)= x³ differentiable? (interval)

A:

Q: For the piecewise defined function None of these 2 what should be the value of c so that we have…

A: In this question we have to find the value of c so that f(x) is left continuous at x=1

Q: Evaluate the limit: lim, ∞ ○-6 00 ○ 6 e 10-00 최승

A: This question can be solved using the concept of L hopital's rule.

Q: The slope of the line normal to the graph y = 2 ln(sec x) at x = is: O-1/2 O non-existent O-2 2

A: The graph y=2lnsecx at x=π4

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

A: Option (b)

Q: Approximate the value of 22.5 O4 + 4 In(2) O4+2 In(2) O 6 O 4 +0.5 In(4)

A: The objective of the question is determine the approximate value of the given value.

Q: Evaluate √xdx f 1+x

A:

Q: Iculate and write a sentence interpreting each of the following descriptions of change. The American…

A: we have to find the change .

Q: Question 2 [ Given the function xye* f(x, y) = 2x³ +50y² a) Find the domain of f. b) Find exist. lim…

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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: dy Find using implicit differentiation. dx Hint: First clear the denominator to get 8x² + 6y =…

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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: 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: 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: Evaluate: f³² ƒ³³ fő cos(# ) dzdxdy J(ㅠ-2) ○ 4 (ㅠ-2) ○ 4m ㅇ 풍 4

A:

Q: Exercise: 11 [ Solve the non-exact differential equations (Apply Rule IV)] 2. (xy³+y) dx + 2 (x²y²…

A:

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

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Q: Apply Newton's Method to f(x) and initial guess xo to calculate x₁, x2, x3. f(x) = x² - 13, xo = 4…

A: