Verify the condition of Rolle's theorem for the function y = f(x) = e xe[-1] ] f'(c) = 0 and find C for which

Q: 1. If f(x) cos(t) dt, then f'(x) =

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Q: Find constants c1 and c2 such that F(x) = c1x sin x + c2 cos x is an antiderivative of f (x) = x cos…

A: To find constant c1 and c2 such that Fx=c1 xsinx+c2cosx is an antiderivative of fx=x cosx. Solution:…

Q: 4. Find the linear approximation to f(x) = cos(x) near a =- [Where L(x) = f(a) + f'(a)(x – a) ]

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Q: Find the derivative of y with respect to x. y = tan (In 3x) O A. 1+(In 3x) 21 O B. x(1 + ( In 3x)) 1…

A: Given: The function y=tan-1ln3x, To determine: The derivative of y with respect to x,

Q: The critical point of the function* f(x, y) = x² + 5y² + 2 cos x

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Q: 9. Find the constants a, b and c of cubic function f (x) = ax³ + bx + c such that : • The slope of…

A: Given that, f(x) = ax3 + bx  + c Slop of tangent line at x = 3 is 0. f'(1) = 24 f(x) croses the x…

Q: 4 - Find the direction A in which the function f(x, y) = x cos y + y sin x decreases most rapidly at…

A: We have to find the direction A in which the given function decreases most rapidly.

Q: 4. Find if y is a function of r defined implicitly by da 2*y + sin a = xe" + In

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Q: Find the directions in which the function f(x,y) = x²y + e* sin(y) Increase and decrease most…

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Q: Find the slope of the curve 2xy = In(e*) sin(x) at the point (2,2)

A: to find the slope differentiate  the equation with respect to x .

Q: 1. Find by implicit differentiation (a) e=/y = x – y (b) sin (x + y) = COs r + Cos y

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Q: Evaluate the second derivative of e22.1.png acos(b/x) f(x) x2 if a = 323 and b = 0.5 at x = 3 using…

A: Given function is f(x)=323cos0.5xx2 Step value is ∆x=0.1

Q: Find the directions in which the function f(x, y) = x²y+exy sin(y) Increase and decrease most…

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Q: Find the differential d4y of the function y=x4.

A: Given function is

Q: Find the linearization of the function y = f(x) = x2 sin(x) at a = π/4 and use it to approximate the…

A: Given,

Q: (1) (a) Find the derivatives of functions f(x) = e2 and g(x) = 5æ?. (b) Compute the definite…

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Q: Find the first derivative of the function below: f(x) = (cos(2a – 7))sin(z+1) %3D

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Q: A. Find the derivative of the function at o P in the direction of A f(x, у) — х — V3sec-1(2xy)at…

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Q: Find the derivative of y with respect to x. y= sin -3 O A. XV1-x - 3 O B. 1+x - 3x 3 c. 1-x -3 O D.…

A: Given that: y=sin-11x3

Q: b) Find O Using the chain rule to find de x-1 dy of y= dy of y sin 1-xy ) Using the implicit…

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Q: Recall the chain rule from differential calculus: f (g (æ)) = f' (9 (æ)) · g' (æ). d dx Find de tan…

A: We have to find

Q: Find the vertical trace of the function at x = 1: g(x, y) = cos√x² + y²

A: Definition : Consider a function z=f(x,y) with domain D⊆R2. A vertical trace of the function can be…

Q: /4 Find the derivative of y with respect to t. (a) y = In(3te-1) (b) y = esin t (In t² + 1) (c) y =…

A: Given functions,  (a)  y=ln3te-1 (b)  y=esintlnt2+1 (c)  y=tlog3e(sint)(ln3) The objective is to…

Q: Find the differential of the function. u = 2x +

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Q: a) Find the derivative of f(x,y) = xe* +cos(xy) at the point (2,0) in the direction of V = 3i – 4 j.

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Q: Find the linearization of the function f(x): L(z)= ab a --4x-5 va a न 4x+3 at z=-1 sin (a) E

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Q: Find the differential d3y of the function y=x2ex.

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Q: Find the differential dy of the given function.    y = x tan x

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Q: The function f(z) = 1 has a poles at z = %3| ez – 1

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Q: Let h(x) = e*. f(x) and assume that f(ln 4) = -5 and f'(ln 4) = 6. Find the equation of the line…

A: We have to find equation of the line tangent to y=hx when x=ln(4)

Q: Let y = In(x'e2x ). Find dy/dx.

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Q: Find the differential d3y of the function y=1/√x.

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Q: Show  that the function Z =1/2(eysinx - e-ySin(x) satisfies the La Place’s equation  =0

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Q: 1. Find the first derivative of y with respect to x (y') of the given functi 1. x³y-xy² +x² +y? = 0…

A: To find the first derivative of y using the given equation.

Q: Verify Young's Theorem S. f(x, y) = = e(2x+y) In(xy)

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Q: 1. 2x'y² + 4yx² = 6. Find dy/dx at (1, 1) by i- %3D

A: Here we have, 2x3y2+4yx2=6 ................... (1)  Differentiate with respect to x

Q: 1. Determine the equation of the tangent line to the graph of f(a) = [² pr+sin r = x = 0. cos (t² +…

A: Above equation of tangent is given.

Q: Evaluate the derivative of e22.1.png acos(b/x) COS f(x) = x2 if a = 71 and b = 0.5 at x = 2 using…

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Q: 13. Find the derivative of the function T(z) = dz +b cz +d numbers such that ad – bc + 0. When is…

A: Hello. Since your question has multiple parts, we will solve first question that means question (13)…

Q: Find the differential dy of each function: a) f(x) = 2x^1/3 - 3x^1/2 b) f(x) = ( x^2 +1) / (x+1)

A: we will find the derivative of given function using basic differentiation rules.

Q: Verify Young's Theorem f(x,y) = e(2x+y) In(xy)

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Q: 2. find the derivative of the function g(x, y, z) = 3e* cos yz,at the point in the direction of A =…

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Q: 11) Find a function y-f (x) that satisfies both conditions: d - 6x -4x+5,f(-1) =3 dx %3D dy 2 3 ==+…

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Q: Find the derivative of function ei, x#0 1 еx, f (x) = 0. at xo = 0 X = 0

A: Find the derivative of the given function.   Given: fx=e1x, x≠00, x=0

Q: Find the derivative of the function: y = In e+2*+1 Oy = x"[(2x(ln x + 1) + 1] y = x*(2 + x + x² In…

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Q: Find the linear approximation L(x) to y = f(x) near x = a for the function. f(x) = sin(x), a = 2…

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Q: A. Find the derivative of the function at o P in the direction of A f(x, y) = x – E) V3sec-1(2xy)at…

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Q: (b). Examine the behavior of e*+iy as x → -.

A: Euler's formula states that for any real number x  Any complex number z = x + iy,  can be written…

Q: 2. If g(x) = x + 2 cos x, then the equation of the tangent line to the graph of g at x = is A. 2y +…

A: Wr have to find the derivative of the given function first.

Q: 2. If g(x) = x + 2 cos x, then the equation of the tangent line to the graph of g at x = is A. 2y +…

A: Equation of tangent line through A(x1 , y1) is given by :- y – y1 = slope x (x – x1)