tan (xy) = ? lim (x,y)→(1,0) y+ xy (a) 0 (b) (c) 3 (d) (e) 1 -/4

Q: az Find if yz – In z = x + y ax

A: To find: The partial derivative ∂z∂x, if yz-ln z=x+y. Calculation: The partial derivative ∂z∂x can…

Q: Let y=tan(4x+6)  Find the differential dy when x=1 and dx=0.1  Find the differential dy when x=1…

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Q: Find partial derivative af dx for the function f(x,y) given below exp 2x. siny .(at the point (In2,…

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Q: find ƒx , ƒy  . 1. ƒ(x, y) = ln (x + y) 2. ƒ(x, y) = sin^2 (x - 3y)

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Q: Find partial derivative føyz of the function f(x, Y, z) = z ln x + 2y

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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: 2. 2. Let そニと X=UV, y = sin v, Use ナ chain chain Rule to find Ev.

A: 1) The given function z=e2x2y+3xy2 Differentiate with respect to x taking y as constant…

Q: Solve using Substitution Method. y(x Tan x + In y)dx + Tan x dy 0

A: The substitution method as follows, y (x tanx + ln y) dx + tanx dy = 0

Q: 2. Let f(x, y,2) = z-sin(xy), x = t, y = In t, z = e. Find derivative of f directly and by using…

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Q: 2. What is the largest possible area of a triangle with its base on the x-axis between x= 0 and…

A: The given curve is y=sinx. To find the largest possible area of the triangle with its base on the…

Q: Let y tan(2x + 2). || Find the differential dy when x = 2 and dx = 0.3 Find the differential dy when…

A: We have to find the differential dy

Q: If f(x, y) = y cos(x) – x* In(y), find the second partial derivative (A dx? -y? cos(x) – 6x In(y) d…

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Q: Find the most general antiderivative of f(x) = -3e" + 10 sec2 (x), where - < x < 2 Note: Any…

A: According to the given information it is required to calculate the antiderivative of the function:

Q: 1. If y=tanx, prove that y=2(y² +1)(3y² +1).

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Q: F(x, y, z) = (6x° sin(y) + cos(18z), xº cos(y), – 18x sin(18z) + 6z°)

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Q: Let y = tan(5x + 2). Find the differential dy when x = 2 and dx = 0.3 Find the differential dy when…

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Q: e'sin" ) *sin sech (x-2) * sech (x-2) F (x) = Explain why g(z) - 0, is not differentialble at a2. if…

A: Here, fx=exsin3πxx2sechx-23

Q: Let z=sin (y 2- 4x). Find the rate of change of z with respect to y at the point (2, 1) with x held…

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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: 4In(Arctan x) = 1-y

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Q: Explain why the linear approximation to ƒ(x) = cos x at x = 0 is L(x) = 1.

A: The linear approximation, or tangent line approximation, of f at x=a is defined as Lx=fa+f'ax-a This…

Q: (i) Find all first and second order partial derivatives of f(x, y) = x²y + cos(xy) (ii) Find lim xy²…

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Q: find dy of X sin 2y =YCO52X

A: Given: x sin 2y=y cos 2x To Find: To find dydx.

Q: d sec z = sec z tan z dz

A: The function is a rule that associates or fixes a number to the particular point z . If , then the…

Q: Find the partial derivative of f(x,y) with respect to y at the point (3,2) f(x,y) = ln(x^2y-xy^2)

A: A partial derivative of a function of several variables is its derivative with respect to one of…

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

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Q: Let y tan(4x + 3). Find the differential dy when z = 3 and dx = 0.1 Find the differential dy when r…

A: y=tan4x+3

Q: What is the result of the partial derivative 3(z² + y sin (z)) Select one: a. 2a + y * cos(x)

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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: Let y = tan (3x + 3). Find the differential dy when x = 3 and dx = 0.4 Find the differential dy when…

A: Given is the function y=tan(3x+3) We need to find the differential dy when x=3 and dx=0.4. and…

Q: (b) 22). Compute the partial derivative frryz for f(x, y, z) = cos(cos(x³ + z²)) + x² In(y² +

A: Given f(x,y,z)=cos(cos(x3+z2))+x2ln(y2+z2).We need to find the partial derivative fxxyz for the…

Q: Given function f(x, y) = 1+ xy - x - y. df a) using partial differential involving limits to obtain…

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Q: Intergrate dy (2y-x) =In Co)

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Q: Determine the most general antiderivative:  f(x) = sec x tan x-2e^x

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Q: dy Use an appropriate technique to find dx from x² + y² = (2x² + 2y² -x)*.

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Q: 1. If y= tanx, prove that y"=2(y² +1)(3y² +1).

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Q: S sin t dt 0. lim x→0 2 x4

A: Given,

Q: dw of w: dt x y Use the chain rule to find the derivative 1 with x cos t, y = sin t, z =- dw and…

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Q: Explain the difference between t dx dx lim + lim s-0+ dx lim dx +

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Q: Let y=tan(3x+3). Find the differential dy when x=5 and dx=0.3  Find the differential dy when x=5 and…

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Q: Find the line tangent to f(x) = 3x + cos(8x) at the point wherex-0. %3D Oy-x+1 Oy-x+3 Oy-11x+1…

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Q: 6y f) limy-0 sin 2y

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Q: Find fyxyx for f(x, y) = ln(xy) − cos (xy) at (1, π)

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Q: Test for homogeneity

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Q: Find the integrating factor μ(x) of y' + 4y - tan(x) = 0 such that μ(0) = 1. μ(x) =

A: See the details solution in below

Q: b)x > 0 impending all continuous f function | f(t)dt = x. arctan(x) f(1) =?

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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…

Q: Use differential calculus to determine the exact position and nature of the stationary points for y…

A: We know that a stationary point of a function f(x) is a point where the derivative of y=f(x) is…

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.