limx→o (t+1)f(t)dt Assume f (0) = 4 %3D 3x2

Q: Find the first partial derivatives for f(x,y)= 9x cos (3xy). of dx

A: To find the first partial derivatives  f(x,y) =9x cos 3xy

Q: dx Evaluate f- +1) using the Cauchy principal value.

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Q: tanx f f(x) = = [tion. A B C √1+1² 1+e' In (secx)√1+tan²x tanx 1+e sec²x 1+ e tanx sec ³x tanx 1+e…

A: Integration

Q: Use the Chain Rule to solve the indicated partial derivatives. Simplify your answers whenever…

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Q: ential equati x²y dy = C

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Q: Q1-Use the chain rule to express dy / dx in terms of xand y: 1-1 a) y = аnd x = at 1= 2 1+1 b) y=1-…

A: Since you have posted multiple questions. I am answering the first one. Please post the question…

Q: Q3:Find all the second order partial derivatives of the f(x, y) = 2x*- 5x'y3-y

A: Given: A function fx,y=2x4-5x3y3-y3. First, find first-order partial derivatives fx by…

Q: Let y=5x^2Find the change in y, Δy when x=3 and Δx=0.2Find the differential dy when x=3 and dx=0.2

A: To find the following parts. 1.)find the change in y (∆y), when x=3 and ∆x=0.2. 2.)find the…

Q: Evaluate: 1-11-24 = - dx 1 + x 0 By the trapezoidal rule with h = 0.5, 0.25 and 0.125 respectively.

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Q: If f(x, y, z) = 12ry - 2yz - 6zx + 7, then the first order partial derivative f = O - (2y – 6x) (2y…

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Q: dy -y2+1,ysCJse Cantial cokditian.

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Q: find dy y = sec-1 (e-x)

A: According to the question, we have to find the derivative of the expression y=sec-1e-x. To…

Q: Find the first partial derivatives of f(x, y) = 4x cos(x2 + y?). %3D

A: Given fx,y=4xcosx2+y2

Q: b) Find the mixed partial derivative at the point (1, 2). g(x, y) = sin(x) In (2y) + y ln(x) + 2xe³x…

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Q: Find the partial derivative. z = sin(2.a*y – 3xy?) az

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Q: lim (z,y) (1,1) 2x – ry – y 22 – y?

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Q: Find the partial derivative. z = (2² + 2x – 6y)"

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Q: 1) y = Arcsin(1 – x²) 2) y = Arctan Vx² + 2x 3) y = Arctan /t²-1 + Arccsc t

A: Given : 1) y = Arcsin (1 - x²) 2) y = Arctan (√x² + 2x) 3) y = Arctan (√t² -1) + Arccsc t

Q: By using chain rule Find dy/dx iff- u=-1, x=-1

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Q: (B) If f(x, y) = x² ye(x+y²). Find the four seconed partial derivative.

A: Let us find the four second partial derivatives of the given function in the next steps.

Q: 1/4 sec2(t) dt J-x/4

A: Given: I=∫-π4π4sec2tdt

Q: psen(x) tan(t) dt lim ctan(x) Vsen(t) dt x→0

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Q: find the first partial derivative  f(x,y) = squareroot (2x+y^2)

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Q: Find the partial derivative. = (a² + 4x – 2y)° - dz II

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Q: Find the first partial derivatives for f(x.y)= 10x cos (3xy)

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Q: Differentiate the function y = 6 + x using the Chain Rule. dy %3D

A: Given, the function is                              We have to differentiate this function using…

Q: Let y = 3x² + 8x + 3. Find the differential dy when x = Find the differential dy when x = 2 and da 2…

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Q: If f(x, y) = y² cos(x) – x³ In(y), find the second partial derivative ду дх

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Q: Find the second-order partial derivative fxx ( x , y ) of the function f ( x , y ) = x 4 y 4 - sqrt…

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Q: d²x dx dx -(1) = 2 4- + 4x = 0 x(1) = 0, - dt2 dt

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Q: 2) Let f(x, y) = x sin(2y) + 5y¹. Find fyyyyyyyyyy (x, y) (10 partial derivatives), explaining how…

A: Here the given function is f(x,y)=xsin(2y)+5y4x. We have to find the 10 times partial derivative of…

Q: ution of yl = x+xy2 W

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Q: Find all first partial derivatives. f(x, y) = 4x2 − 2xy + y2

A: Consider the given function  fx,y=4x2-2xy+y2

Q: b) Use the chain rule for partial derivative to find 2 when z = f(x, y) = x²y + ln(x + y) and (x, y)…

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Q: d²x dx + 4 + 5x – 10 = 0, when t dt 0, x = 0, x = 0 %3| %| dt2

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Q: 2x lerivatives from first principle, find the derivatives of y = 5 V3x-e2x-(xln x)(In(In x)) -2e2x)…

A: We have to find the derivative from the given function

Q: Use the chain rule to find dy/dx for th following (a) y= (3x^2 - 13)^3

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Q: Q2: Find Partial derivative of the function with the respect with each variable f(x, y) = (x² - 1)(y…

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Q: S sin t dt 0. lim x→0 2 x4

A: Given,

Q: Find both first partial derivatives. z = 6x − x2y + 8y2

A: Find both first partial derivatives. z = 6x − x2y + 8y2

Q: 1-fd dydx R = {0,1} * {2,5} y2 2-S y2 (1–5x)2 dxdy R = {0,1} * {0,2}

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Q: dy ifx²y + secy Find dr In x .

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Q: d rIn(x) t tan(t) dt|. dx -1

A: we have to evaluate the following

Q: If z = xy2 + 6x, then y2 + 6 is the first order partial derivative of z with respect to x. O True…

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Q: Let y = 3x² + 8x + 3. Find the differential dy when x = 1 and dx = 0.2 Find the differential dy when…

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Q: (b) Form the partial equation by eliminating function f from z = f(x?

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Q: tan Зy limy 0 3y O 3 O undefined

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.