pose that f: R → R is differentiable at c and f(c) = 0. Show that f (x)| is differentiable at c if and only if f'(c) = 0. %3D

Q: Find dwl dt at the given value for the following functions 1) w=x+y, x= cos(?), y = sin(t), at t = 7…

A: We have to use properties of trigonometric functions.

Q: Let A E R"Xn, let b e R", and let n n f (x) = xT Ar + 6Tx = Aikr;xk +> b;x;. i,k=1 i=1 Show that f :…

A: Definition: A function f:ℝn→ℝm is differentiable at x0 with derivative M if M:ℝn→ℝm is linear and…

Q: What is the maximum value of f(t) = sin t + cos t in the interval 0<t< =?

A: Given; f(t) = Sin t + Cos t.

Q: If sin(x) f(x)= 68+t2 dt Jtan(x) and g(y)= f(x) dx , Then g) is equal to

A:

Q: If f(x) = xe , x >0 and (Y = ln(X)), then the PDF of Y is %3D (In(1)² (In(y))e ye

A: Answer: ⊙ ey-12e2y

Q: the linear approximation for f(x,y) = sqrt (y+cos^2 x) at (0,35) is ?

A:

Q: af dy of f(x, y) = tan (x²y³ + 2xy)? What is the

A: Given:     To determine:

Q: Assume that x and y are both differentiable functions of t. Find dy/dt when x = 16 and dx/dt = 9 for…

A: Solution is given below:

Q: Find the linearization of the function f (x) = x at x = 1. a lal sin (a) L (x) Using this…

A:

Q: - Find the Linearization of f (x) = sinx at a 5. Provide your answer as L(x) =? %3D %3D

A:

Q: dz is equal to .. dt Let z= In (x2+y²) where x=ue"sin t and y = ue"cos t. If u= -2 and t=0 then -

A:

Q: Assume that x and y are both differentiable functions oft and find the required values of dy/dt and…

A: Given :  x 2 + y 2 = 169  Find dx / dt and dy / dt

Q: Assume that X and Y have joint pdf Sr + 3x?y if 0 <r<1 and 0 < y < 1, f(x, y) = %3! otherwise.

A: We know that, Covariance(X,Y) = E(X).E(Y) - E(XY) Here E(X) and E(Y) are given so we'll Calculate…

Q: Find dydx? for f(x, y) = eXy

A:

Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

A:

Q: dz If z = e2x+ 3y and x = In t, y = t2, calculate from the total dt derivative formula and show that…

A:

Q: Find the derivative, dy/dx: In-2x O y = -() In' 1-4 la > 是 In' x 2/1+2In ४ In' z In z 2w In² z ) In'…

A: This question is based on diffrentiation.

Q: Let f(x) = sin? (x). Define F(x) | f(t) dt. What is F" -) ?

A:

Q: ) Find the linearization of f(x) = sinx at x = 0.(b) Compute dy if y = x2 +x and x changes from x =…

A: Since you have submitted two questions, we'll answer the first question. For the second question…

Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

A:

Q: True or False: For an IVP dy/dx = f(x,y); y(a)=b, if f(x,y) is not continuous near (a,b), then its…

A:

Q: as f(z) = e e analytic %3D

A:

Q: Where is the function f(x, y) = e' arctan (VI+In(x+y)

A: In this question, the concept of continuity is applied. Given function is fx,y=etan-11+lnx+y

Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

A: Given : Equation x2 + y2 = 25 and x and y both differentiable functions of t.   To find : (a)…

Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

A: Given y=3x2-5x a. We need to find the value of dy/dt when x=2,dx/dt=3. the value of dy/dt=21 when x…

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

A:

Q: Let f(x, y) = 6e sin(7y) af af dy

A:

Q: Suppose f is a differentiable function of x and y, and g(u, v) = f(e" + sin(v), eu + cos(v)). Use…

A:

Q: Find fr and fy- f (x, y) = 4etlo dt f#(x, y) f„(x, y) =|

A:

Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

A: Given function is y=2x2-3x. (a)To find dydt when x=4 and dxdt=1. Differentiating the given function…

Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

A: partial differentiation

Q: Let f(x, y) = 3e" sin(5y) af af dy

A:

Q: Assume that x and y are differentiable functions of t. Find  dx/dt given that x= -3 , y= -2 , and…

A:

Q: If f:R⇒Rf:R⇒R is defined by f(x)=e−cosxsin(x)f(x)=e−cos⁡xsin⁡(x) for every x∈Rx∈R then…

A: The given function is: f(x)=e-cos x sin x To find the derivative first. f'(x)=ddxe-cos x sin x…

Q: Suppose z = f(x, y) is a differentiable function of x and y, x =r cos 0, and y =r sin 0. (a) Compute…

A:

Q: b) f(x): 1 + sec2

A:

Q: Let sin(r-y) ||| + \y| +0 (x, y) = (0, 0) f(x, y) Is f continues at the origin? Why?

A: Solved below

Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

A: Differentiate both sides with respect to t. Then plug x=4 and dx/dt=1

Q: Find the antiderivative F for f(x) = | sin z|, -T <x <0 satisfying F(0) = 1. (1) F(x) = - cos x – 1…

A:

Q: Suppose f(z) = 1 + sinz and F is an antiderivative of f that satisfies F(띠) =D0. Then F(z) = - COSX…

A: Integrating f(x).

Q: if (2,y) # (0,0) Let f(x, y) = aª + yª Show that D1f(0,0) and if (2,y) = (0,0) D2f(0,0) exist but f…

A:

Q: If z=f(x,y), x= r cos θ and y= sin θ, where f is a differentiable function expressing az/ax and…

A:

Q: If f(x, y) = x cos y + ye", find the second-order derivatives %3D af a²f ах ду" and ar" dy ax'

A:

Q: Find the antiderivative F(x) of f(x) = 8(sec x)(sec x – 4 tan x).

A:

Q: Suppose f(x) = x² + sin æ and F is an antiderivative of f that satisfies F(T) = 0. Then F(x) =

A: Solution..

Q: Is 2xy x++y2 (xy) = (0,0) fle.y) = (xy) = (0,0) continuous at (0,0) ?

A: Here f(x,y)=2x2yx4+y2    , (x,y)≠(0,0)     0           , (x,y)=(0,0)For continuity,…

Q: Suppose F(x, y) = 0 and y is a differentiable function of x. Explain how to find dy/dx.

A: It is given that F(x, y) = 0 and y is a differentiable function of x . For the function F(x, y) = 0…

Q: implicitly dx

A: Solved below

Q: Find the linearization of the function f (x) = =° at z = 1. L (1) = Using this linearlization, ƒ…

A:

Q: Let flx.y)a gxy? ty? 9x+y (4,y)+(0,0) 1. is f continuOus at (0,01? why?

A: The Given function is: The function f(x) is continuous if its limit exists and the limit value and…