|x? +3x +1 ax + In x+b ,x21. „r<1; Let f(x) = If function f(x) is differentiable at point x=1, then what is the value of a+f'(2) ?

Q: (x2 -7 , 0b Is fdifferentiable at b?

A: Given that: f(x)=x2-7,       0&lt;x≤b6/x   ,        x&gt;b

Q: [sin (zx), 0<x<1 lax+b, 1<x<4 17. Let f (x)= { f(x) is Find the values of a and b such that…

A:

Q: Find all points (x, y) where f (x, y) has a possible relative maximum or minimum. Then, use the…

A: Consider the given function. fx,y=2xy+y2+2x-1 Find the derivative with respect to x. fx=2y+2 Put the…

Q: f(z) is a twice differentiable function with f(0) = 1, f(2) = 4, f'(2) = 5, Then af"(x)dx = %3D

A:

Q: Determine the value of a such that f is differentiable at x = 1. for x <1 a sin(x-1)+6 for x21 S(x)…

A: given , f(x)=x+22-3      for x&lt;1asinx-1+6      for x≥1 we have to determine the value of "a" such…

Q: 3 Let f(x) = 2 + In(bx), where b is a positive constant. Find f'(x).

A:

Q: 1) Find the absolute extremum values of f(x) = x? [1, 2]. 2x +24 over the interval %3D -

A: Topic - maxima minima

Q: 3. Consider the function f(2, y) = x° + 7a? + 2æy + y? – 19r – 4y + 1. Find all critical points of f…

A:

Q: 2. Let f(x) = S dt for x 2 2 In a) Find F'(x). b) Is F increasing or decreasing? What can you say…

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Q: find the absolute extrema of thefunction on the closed interval y=x \ln (x+3),[0,3]

A: A function is usually represented as f(x) where x is the input to the function and f(x) represents…

Q: Find the linearization of the function f (x) = x' at x = 1. a ab Va |a| sin (a) 7 х-6 L (x) Using…

A: Given a function,

Q: Let f(x,y)=3x2-2xy+y2-8y  Find the absolute extrema over [0,1]x[0,2]

A: Consider the given function fx,y=3x2-2xy+y2-8y First, find the partial derivatives of the function…

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

A:

Q: 13. A differentiable function f on the interval -2 sxs7 is such that f'(c) = 0 where -2 <c<7. If…

A: Clearly we have, f'(c) = 0. Means c is a critical point.

Q: x - y -2x Prove by definition that for f(r, y) fy(x, y) = %3D x+ y' (x+ y)2

A:

Q: 11. Find the linear approximation of f(x) = √√x_ at a = 1. Use the linearization to estimate the…

A:

Q: f(x, y) = In (x²y - x) %3D

A: Here, the given function is: f(x,y)=ln(x2y-x) First to find the first derivatives:…

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: Let f(x,y)=3x2-2xy+y2-8y  Find the absolute extrema over [0,1]x[0,2].

A: We have f(x, y)=3x2-2xy+y2-8y find critical points ∂f∂x=6x-2y=0 ... (1)∂f∂y=-2x+2y-8=0  ...(2)solve…

Q: If f(x)= (x^4) + 3x + 1 and there are two roots x=a and x=b in the interval [-3,-1] with a &lt;b.…

A: The given function is,

Q: (c) A non-constant function f : [0, 1] →R such that f(x) > 0 for any r € [0, 1] but | f(x)dx = 0.…

A:

Q: 10. Consider the function defined by f(x) = Vr. Is ƒ differentiable at r = 1? at r = 0? at %D x =…

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Q: Find the local linear approximation of f(x)= at 2+ x xo = 2, where Ax = x – 2. NOTE: Enter the exact…

A: while finding out the local linear approximation of any function f(x), what we do is to determine…

Q: Q3) For what values of a and b are -x* +а, xsin + 1 0<xs y = bx3 + 2 , Continuous at every x ?

A: Explanation of the answer is as follows

Q: Find a point zo where the function f (z) = (z – 8 – 10i) (z – 8 – 10i) is differentiable. What is…

A:

Q: If f is differentiable everywhere and f(1)=f(2)=π, then ∫12 f'(t)dt=0   True or false?

A: True because,

Q: 3. Show that x? if x>0 0 if x<0 f(x) = is differentiable at xo =0 but f' is not differentiable at xo…

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Q: if x 0 f' _(0) f',(0) Is f differentiable at 0? Yes No

A: To find f is differentiable at 0 or not

Q: 25. Use the definition of differentiability to prove that the following function is differentiable…

A: First let us find the partial derivatives of the given function f(x,y)=x+y as shown below:…

Q: 25. The function g(x) = [", |u| du is not differentiable at x = 0.

A:

Q: 2. Find and classify all the extrema of the function f (x, y) = 4xye e-(x²+y²)/4

A: The given function is:  f(x,y) = 4xy e-(x^2 +y^2)/4

Q: Find absolute maxima and minima of the function f(x, y) = x² + y² on the closed triangular plate…

A:

Q: (c) Does there necessarily exist a differentiable function h with 0 < h(x) <1 and E = {x : h(x) = 0}…

A: Sol:in the given question we have to tell about the differentiable function f(x)s.t whose range is…

Q: Find a multivariable function f(x, t) that satisfies the Black-Scholes equation: ft = f - xfx -…

A: f(x,t)=etlog(x) satisfies Black-Scholes equation: ft = f - xfx - x2fxx

Q: 9) A function y(x) is increasing and has upward concavity on the interval [-2, 3]. Would a…

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Q: 7 For the function eX, the linear approximation around x = 2 is %3D

A:

Q: Differentiate f(x) = ax? with respect to x. Assume that a and k are positive constants. k+x f'(x) =…

A: f(x)=ax2k+x We need to find the derivative of the given function.

Q: xY 2. (a) Prove that the function f(x, y) is differentiable everywhere in its do- %3D x2 + y? main.

A: Solution is given below:

Q: 9. 3x2 Let g(x) = -2x2 r<0 (b) Prove that q is not differentiable at 0.

A:

Q: 3. Find constants A and B such that the function x2 f(x) = if x 2 is differentiable at x = 2.

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Q: 2 f(x, y) = x² + 3xy

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Q: Find f fy. - f(x.y.z) = x - Vy² + 22? + 2z² = (Type an exact answer using

A: Here we have to find fx , fy and fz  of

Q: if f(x)=integral t^3+5t^2+6, from 0 to x. what is f''(x)=?

A:

Q: (3) If | f(x) dx exists and c is a real constant, prove that f(2) dz = / f(x + c) dz. | {(x+c) Vel

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: Find f(3,4) for f (x, y) = In(x + /x² + y²). %3D

A: Given:- f(x, y) =ln(x+√(x2+y2))  To find:- fx(x, y) at (3, 4)

Q: 3. Let f)=x+x+2x-1E2,lx). Then x= 1 is a root for r() of mmltiplicity 3D1 None 4 2

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Q: 3. Proof that f (x) = x sin is continuos but is not differentiable at 0

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.