10 10y-y² IN - 10y-y² ex² + y² dxdy

Q: Find y' y = e2x - e3x e4x

A: This question is based on diffrentiation of exponential Function.

Q: What is the derivative of y = (3x + 1)? 21 dx dy = 6 (3x + 1)²¹ dx 6 (3x + 1)² dy dx = 7 (3x + 1)6…

A: To find the derivative of the given function

Q: How do you evaluate this integral using trigonometric substitution?

A: Here x2 -a2  type we use trigonometry substitution by x=a sec(θ)

Q: x -2x +x= 15; x (0) = 7, x (0) = -16

A: This question is based on diffrential equation solved using Laplace transform.

Q: 5. 1-cos2y 1+cos2y dy

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Q: Using the laplace transformation table, evaluate the following, considering any other variable other…

A: This question can be solved using the concept of Laplace transformation.

Q: Given w = xe¯ª + ln(x²yz³). Determine δω ?х ?w dx 2 = -xe tết xyz³ dw = xe¯* + 1 + 1²/12 8x dw…

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Q: 니 - ****** سر ** x² coscyldy dzdx

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Q: L’Hopital

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Q: Given a function, Based on the function, F(s) = 3s-6 s² +8s+7 a) Determine f(t). b) Based on…

A: Given a function, Fs=3s-6s2+8s+7Based on the function, a To determine ft.b Based on solution ft…

Q: Use a table of integrals to evaluate the following indefinite integral. The integrals may require…

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Q: The graph of } = xe-r is symmetric with respect to the Origin None of these the x-axis the y-axis

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Q: Evaluate the integral. The integral from 0 to t of 9sin^2(x) dx  Then determine whether the…

A: A detailed solution is given below.

Q: Find the Taylor series expansion of f(x) = ln(3-2x) about a = 1.

A: The function f(x) is given by, f(x)=ln(3-2x) Differentiating the function successively upto n…

Q: Find the limo (cos x) = Show your complete solutions. No shortcuts.

A: Given,  limx→0cos x1x2

Q: aw C. If w=f(x,y) and x=r. cose, y=1. sing. Prove that ar 1 (dw r² 20 = fix² + fy²

A: Let's prove.

Q: 3- اول ** X 2 Sin² Lys y

A: Follow the procedure given below.

Q: Evaluate the given limit. Show your complete solution. limx→∞ [e5z + x²]

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Q: 2.) Find the volume of the solid generated by rotating the region enclosed by y = x + 3, y = 0, x =…

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Q: Estimate the following definite integrals using the Trapezoidal rule and Simpson's rule. Estimate…

A: Trapezoidal rule:-∫abf(x)dx=∆x2{f(x0)+2f(x1)+2f(x2)+...+2f(xn-1)+f(xn)}where ∆x=b-an, n is the…

Q: Find h'(-3) if h(x)=4g(x)-5f(x), f(-3)-7,and g'(-3)=-2. Oh'(-3)-0

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Q: f(x) = 2²3 on (0, ∞) x+3

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Q: Find the area between the y-axis and the graph X = Y 7 6 5 4 X 543-2/1² 1 2 3 4 5 WŃ y - 1 on the…

A: Here we have to use the concept of integration

Q: dx 3. If 8c²xy = (x² - y2)2, find- dy

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: In the year 2000, the population of a small city was 40,000. The population grows at a rate of r(t)…

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Q: Find the general solution of the given differential equation. xdy-y=x² sin x yw Give the largest…

A: Explanation of the answer is as follows

Q: 3. Consider the vectors X and Y in R³ where X = i +3j and Y = 4i - 2j+2k. Find the unit vector…

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Q: 1. If f(x) = sinx, show that f(x + y)-f(x) = cos x siny - 2 sin x sin² 2 2Y-T

A: 1) Given f(x)=sin(x)

Q: What is the equation of the tangent line to the curve y = √2 +16when x = 3? V x-10y +47=0 3x-25y-116…

A: SOLUTION-

Q: 2x³ is an antiderivative of what function? y = 6x² y = -6x² X y = y = - 2 X 2

A: 2x3 is an antiderivative of what function.

Q: A triangle is measured and two adjacent sides are found to be 3 inches and 4 inches long, with an…

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Q: D Question 8 For the function y = (x - 2) Inx what are the two x intercepts, and between the two…

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Q: -Expand Fourier series in cosines only defined by: (15 f(x) = π-x, 0<x<T 1 B

A: This question is based on formulaof Fourier Cosine series.

Q: 3) The line L: x = 3 + 2t, y = 2t, z = t intersects the plane x + 3y -z = -4 in a point P. Find the…

A: This question is based on 3-d geometry.

Q: If c is a constant, what is the limit of c as x approaches a? 0 C a X

A: A detailed solution is given below.

Q: 11. Use L'Hopital's rule to find the following limits. x² + 3x-4 x-1 (a) lim x-1 In x xx-1 (b) lim

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Q: What is the lim→( For answers that are fractions infinity negative infinity 7 sec (7x) cos(3x)?…

A: See the details solution in below

Q: Give an equation of the vertical asymptote of O y = 2 ○ y = 0 O There is no vertical ymptote. Ox=0 y…

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Q: 12 Let A be a square non-invertible matrix. Which of the following is not true? Select one…

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Q: 3. fe+tanx+(tan²x)+taxdx

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Q: Whatis the derivative of y = sin (2x − 1)? dx = 2 cos (2x - 1) dy dx = cos 2x dy -2 cos (2x - 1) cos…

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Q: Instruction: Evaluate the following Integrals. Write your COMPLETE solutions neatly and organized.…

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Q: What is the limo+ sin(y) In(y)? For answers write... that are in decimal form and round off to…

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Q: What makes a function f(x) continuous at x = c? I. f(c) is defined lim f(x) exists II. X-C III. lim…

A: The function f(x) is said to be continuous at x=c if: I) f(c) is defined. II) limx→cf(x) exists.…

Q: (i) Evaluate the limit or show that it does not exist. 2xy lim (x,y) (0,0) x2 + 2y² (ii) If cos(xyz)…

A: Firstly we can find Limits and In second one we can find partial derivatives .

Q: Q4/ Answer two from the following :- 4- Evaluate and change the order of integration in 1 = ²*xy…

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Q: 15. Yogurt containers can be shaped like frustums. Rotate the line y = x around the y- axis to find…

A: 15.   yougurt containers can be shaped like frustrums.Rotate the line y=1mx around the y-axis…

Q: For the next three series, (a) determine the radius of convergence, (b) determine for which the…

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Q: B. 2x³ +2y-3y² = 13x Steps 1. Take the derivative of both sides with respect to x. 2. Since the left…

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Q: Gym A Gym B Total Monthly Cost vs. Number of Visits C Number of Visits Total Monthly Cost 10 55 70-…

A: Linear cost