y = x2 - 2x over the interval (0, 2]:

Q: Use differentiation rules to find y' = dy/dx.

A:

Q: Find the linear approximation at x = 0 to Write your answer in the form y = Ax + BỊ.

A:

Q: Find all the points of g(x, y) = x³ − 3x + 3xy² where a relative extrema might occur.

A:

Q: On what interval is the curve t2 X. dt y% = Jo t2 + t +2 concave downward?

A:

Q: Let f(x, y) = 12x² + 7y² + 3x + 3y+ 6 Find D = frz · fy – fåy-

A:

Q: find f given f (z, y) = e + 2ry 4y at (0,3)

A: Topic- partial differential

Q: of of and dy 6. For the function f(x.y) = sin ° (6x - 5y), find of df dy II

A: In partial derivative when take the derivative with respect to one variable consider other variables…

Q: Fundamental Theorem of Calculus.

A: ∫abfx dx

Q: d²y nd by implicit differentiation if 3x² – 7y? = 14. dx?

A:

Q: Use the linear approximation of f(x) = at r = 0 to approximate f(-0.1). 1+r

A: Use the linear approximation of f(x)=1/(1+x) at x=0 to approximate f(-0.1).

Q: [F-dš where F = xỉ – y°j+(x+ y+z)k

A:

Q: Find f, fy. f- f(x.y.z) = 3x - 4y 2. 2 +z?

A:

Q: of of For the function f(x,y)% 9x2- 3y°-4, find and dx dy of II

A: While calculating the partial differentiation of a function with respect to X we consider the other…

Q: Find the length of the curve y = Vcos 2t dt from x = 0 to x = T/4.

A:

Q: 4. Use the contour integration to find f G dx. 1 x4+16

A: Answer: π/(16√2)

Q: Find the linear approximation of the function f (x, y) y- 1 at (0,0) x + 1

A: We are given fx, y=y-1x+1. Here, we need to find linear approximation at (0, 0). Now, fx=∂∂…

Q: of and dy For the function f(x,y) = In (8x + 9y), find - - of

A: partial derivative of two variable functions

Q: dy 2- Find for the following function: dx А- у%3Dх*. сosx B- y= 2(secx)²

A: Given : A) y = x3·cosxB) y = 2secx2

Q: Q4) Find y" + 3y' 5y at x-5 where y = xsin(1/escx))

A: To find the y"+3y'×5y at x=5  Given y=xsin(1/cscx)

Q: xy ,show that: x- y If z = = 0

A:

Q: 2. For what value of k will x – iky F(x, y) = (x+ y)² + be analytic?

A: Given function is fx,y=x+y2+x-ikyx+iy If it is analytic then it satisfy C-R equation ux=vyuy=-vx

Q: Find the linear approximation at x = 0 to Write your answer in the form y = Ax + B.

A:

Q: find given f (x, y) = eª + 2xy² – 4y at (0, 3) af dy'

A:

Q: Find f, and f,. f(x, y) = 13x In xy

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Q: Use implicit differentiation to nd dxidb. x3+ 2x Zy+y3=8 x2.3y x2 3xy x2 2

A: To differentiate with respect to y x³+3x²y+y³=8

Q: y = vx from x = 0 to x = 4 and the x axis %3D

A: Given curves are  y=√x  x=0 to x=4 and the x- axis   We have to find the bounded region area .

Q: of For the function f(x.y) = In (x + 6y), find- of and dy

A: It is partial derivative so when we differentiate with respect to one variable consider other…

Q: Find the linear approximation of the function y = x at point xo = 1 .3 О а. у%3D Зх - 2 О Б. у3D 3х…

A:

Q: Find for F(X,)= Sin xy+ T Y²-x = 0

A: Given query is to find the derivative of the expression.

Q: Find of the function f(x,y) = sin(x²y³). əx3

A: The product rule of differentiation : (PQ)'=PQ'+QP' sinx'=cosxcosx'=-sinxxn'=nxn-1 Use the given…

Q: Find relative extrema for f(x,y)=x^3 - 6xy + 8y^(3) - 2.

A: Question- Find relative extrema for  f(x,y)=x^3 - 6xy + 8y^(3) - 2.

Q: of of For the function f(x,y) = 4x* - 3y' - 8, find and dx of %3D dx of

A:

Q: of find 4x + 9y of and dy For the function f(x,y) = %3D of dx ||

A: We can answer this question as below

Q: - x'yt, show that fxy = fyx. 7,4 Given f(x, y) = et*

A: Given f(x,y) = e(x^4y^9) - x7y4

Q: Assuming 9x° – 5y - 4xy = 0 defines y as a differentiable function of x, use the theorem dx - to…

A: Given: 9x3-5y2-4xy=0 We have to calculate dydx(1,1) by the given formula.

Q: Use differentiation rules to find y' = dy/dx.

A: Consider the equation

Q: Find the differential of y=x^4-2x^2

A: Given query is to find the differential of the expression.

Q: Supposed that z is defined implicitly as a function of x and y by the equation x2 + y2 +z2 = 4. Find…

A: The given data is: x2+y2+z2=4 To find the value of dzdx

Q: Suppose that f(x, y) = sin(4x + 6y) is a function of two variables. %3D

A:

Q: Find the interval on which the curve 1 dt 4+t+ 2t2 is concave upward.

A:

Q: Find the linear approximation 0 to Write your answer in the form y = Ax + B. at x =

A: Explanation: The Linear Approximation should be a line that can substitute (in a narrow interval)…

Q: Q11) For the z= (2x+3y)10,which is correct ?partial derivative

A: Given,  z = (2x + 3y)10 To find the partial derivatives.

Q: Q4) Find y" + 3y' 5y at x-5 where y = xsin(1/cscx))

A:

Q: Find the linear approximation of f(x) = Vx at xo = 27.

A:

Q: dy when x = 2 dt х = x + 4, find y

A: Differentiation. ddx(f(x)g(x)) = g(x)×f'(x) -f(x)×g'(x)g(x)2 Where, f(x) and g(x) are the function…

Q: 3 Q1// :- find fy,fy at point (4,1) for f(x,y) = Xe

A:

Q: Found the line of differentiability of f(z)=x2 - 2xy + 3y + i(2xy - y2 +x)

A: Answer

Q: 3. For x= In /t y=t2, find y'-y"when x=0.

A: To find: The value of y'-y" when x=0 . Given: The value of function are x=ln(t) and y=t2. Formula…

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.