find (Ix - xl) vx€ (-1,1) and x # 0. dx (b) Test the continuity of the function f(x) = sgn(lxl) at x = 0. Is f(x) differentiable at x = 0? Explain that.

Q: Let f(x, y) = sin(x+ y²). Compute the rate of change in the direction of fastest decrease for f at…

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Q: Use differentials to approximate the change in y = f(x) from x = 4 to x = 4.1 for the function, f(x)…

A: It is given that,

Q: 9) Where is the function ht) = (t+ 5) differentiable?

A: Given         h(t)= t+51/3

Q: Find the derivative of the function at P in the direction of A g(x, y) = x - (v² /x)+ /3 sec*(2xy),…

A: To find: The derivative of the function at P0=1,1 in the direction of  A=12i+5j Given information:…

Q: Find the MacLaurin polynomial of degree 7 for the function sin (ot) dt. F(X) = %3D

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Q: Use implicit differentiation to find y' at (2, 0) for 2x2 + e2ay

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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: Let f(x, y) = sin(3x + 5y) and P = 3 Find the maximum rate of change of the fucntion f at the point…

A: Find gradient of f(x,y). Find compute the point . Take the magnitude of the same .

Q: Assuming - 6x° -y² + 7xy = 0 defines y as a differentiable function of x, use the theorem Fx to find…

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Q: Fnd the domain of continuity of flay) (a.y)#l0,0) ; (xy)=l0,0).

A: 3x2yx2+y2; x,y≠(0,0)                             f(x,y) =                    0…

Q: A:- Find the orthogonal trajectories for functions In -1) = - COS X +a y

A: The given family of curves is: lny-1y=-cos x+a ,            where a is an arbitrary constant.

Q: Dicuss the contiunity of the function f (x,y) = ln  (x+y-1)

A: We know: 1) Polynomials are continuous everywhere. That is, at every point in real number 2) Sum of…

Q: QIFind the derivative of the function f(z, k) = z* – 16k + tanh(z) – 4 csc(k) in terms of z and k ?

A: Dear student  Here is the solution of your query

Q: Approximate X f(x) = e*over the interval [- 4, – 2] using 2 subintervals.

A: In this problem, Simpson 1/3rd rule is used to find the approximate value of e^x over the interval…

Q: Supose z is implicitly defined by the equation qy+ 3x + xyZ + 32=9 in an enmrament of the point…

A:

Q: Find the derivative of the function at Po in the direction of A. 1- f(x, y) = 2xy - 3y² , Po ( 5,5),…

A: As per our guideline we are supposed to answer only one question you can repost other in next…

Q: Use the second derivative test to find the local extrema of the function f(x, y) = x+ 2xy – 6x –…

A: Step 1: Find the partial derivativesfx and fy and put both equal to zero and we getcritical points…

Q: Find the linearization L(x) of f(x) = cot(x) at x = π/4.

A:

Q: What is the linear approximation of the function f (x) = e x at x = 1?

A:

Q: B1. Verify fy = fx for the function f(x,y) = ln(2x- 3y). %3D xy

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Q: Find the derivative of the function at Po in the direction of A g(x, y) = x - (y/x) + V3 sec (2ry),…

A: Let us consider the given function z=f(x,y) The directional derivative of the function at Point P in…

Q: 2. Is the function G(x) = 2e -5 an antiderivative of the function g(x) = 6e"? Use the…

A: Given information: function Gx=2e3x-5 function gx=6e3x here, we have to show that, the function G(x)…

Q: fro(x- dt show that = f(x). dx y 3

A: y=12∫0xft x-t2 dt

Q: Find the linear approximation to the function f(x, y) = sin y --- |T at x, = (1, -2) 2 and use it to…

A: The solution is given as

Q: Use the definition of the derivative to show that the derivative of y = f(x)3 2/ is 1 f'(z) = VI %3D

A: GIVEN f(x) = 2√ x CALCULATE f'(x) = 1/ √ x

Q: Find the derivative of the function at P, in the direction of A g(x,v) = x - (y² /x)+ V3 sec (2xy),…

A: Given that  g(x,y)=x-y^2/x+√3arcsec(2xy) P(1,1) and A=12i+5j To find the directional derivative of g

Q: Find the derivative of the function at Po in the direction of u. f(x, y) = In( 6 x - 3 y), Po(-7, -4…

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Q: Let = (x – 3)(x – 1)2 for a differentiable function f which is defined on the interval [0,4]. %3D dx

A: TO FIND THE CRITICAL POINTS, INTERVALS OF INCREASE AND DECREASE VALUE OF 'X' AT WHICH LOCAL EXTREMA…

Q: 1. a- Find a result by using variable separation for ý=secy h- xy = x + y

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Q: Let y be a function of x and suppose y=In(x²+y²). What is the correct result for the derivative of y…

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Q: Calculate the derivative of the following functions

A: Given: y=fx gx5 To determine: Derivative of the given function

Q: Determine k so that f(x, y) = kx(x- y) for 0<x <1,-x< y<x is a joint pdf.

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Q: Find the interval in which function f(x)=sin (log,x)+cos(log,x) is decreasing

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Q: Find the linearization L(x) of f(x) = cot x at x = 4 %3D -

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Q: Find fx, fy. Verify your answers using computational tool. f(x, y) = ½ In (x²+ y² ) + tan' (y/x)

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Q: Using the definition, find the derivative of fz) = 3 z^-6 z² at point z= 0

A: Given,          fz=3z4-6z2

Q: Find the derivative of the function at the given point in the direction of A. f(x.y) = 6x+10y,…

A:

Q: Let y = f(x), where   f(x) = 5x3/2 + x1/2.   Find the differential of the function.

A: The given function is

Q: use implicit differentiation to find ay for x°-xy+y°=4.

A: Use chain rule to differentiate the middle term.

Q: Find the derivative of the function at Po in the direction of A. g(x, y) = x- (y/x) + V3 sec (2xy),…

A: we have to find directional derivative.

Q: Find the linear approximation of f(x) = Vx-1 approximate 2.02. near a = 2. Use the result to

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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: Let f (2) = – z). (7z+ 10) (i

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Q: Find the derivative of the function at Po in the direction of A. f(x,y) = 4xy – 4y“, Po(-2, - 8), A…

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Q: Determine the length of the curve TC f(x) = In[sec(x)],0 < x < 4

A: The given curve is- f(x)=lnsec(x)Interval 0≤x≤π4We need to determine the length of the given…

Q: find the derivative of the function at P0 in thedirection of v. ƒ(x, y) = 2x2 + y2, P0(-1, 1), v =…

A: Given: fx,y=2x2+y2  We know that, The direction of v is the unit vector obtained by dividing v by…

Q: The gravitational force exerted by the planet Earth on a unit mass at a distance r from the center…

A: To find the continuity of F(r).

Q: Find the interval in which function f(x) =sin (logex)+cos(logex) is decreasing

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Q: Find the derivative off with respect to x of f(x) = In x⁹. The derivative off with respect to x of…

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Q: The derivative of f(z) = Log(2iz - 4+6i) at z = -3+i is

A: