your to nod of a. f(x) = x – 4x-*², I[1,2]

Q: The tangent line to y=f(x)y=f(x) at (−3,−2)(−3,−2) passes through the point (−4,−3)(−4,−3). Compute…

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Q: Verify Rolle's theorem for f(x) = x* – 4x+8 over the interval [0, 2].

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Q: of f(x, y, tion of ve

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Q: Verify that fy=f for the following function. "yx 5,3 6,4 f(x, y) = 2x°y³ - 8x°yª 5,4 = 10x*y³ –…

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Q: Find the derivatives of the functions in Exercis

A: We have, f(x)=7+x sec x First, we write the above function in power form. fx=7+x sec x1/2

Q: For what value(s) of x is the function f(x) = } 2x + 4 (x² +x +1 if – 2 sxs1 if x>1 NOT continuous?

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Q: Suppose that f(x, y) is continuous at (2, 3) and that f(2, y) = y3 for y ≠ 3. What is the value f(2,…

A: Given that f(x, y) is continuous at (2, 3) and that f(2, y) = y3 for y ≠ 3. We have to find the…

Q: Use the sign of the derivative to establish the inequaltiy In(1+x) > I -,V> 0. 2

A: See the attachment

Q: The function f(x,y) =26-2x²-y² is continuous at point (2, -3). .A True .B False

A: The objective is to determine whether the statement, " The function fx,y=26-2x2-y2 is continuous at…

Q: 2. f(x) = Vx – 1 at x = 5

A: Function is continuous and differentiable both at x= 5.....for detail...go through the solution

Q: If - 2x +1 ,when X#! and fcx)= 3 when x= 1 show that The function fex) Continuous at X - 1

A: The detailed solution is as follows below:

Q: The function f(x) = x^2 is decrea sin g on (- ∞,0)  True or False

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Q: Find the derivative of the transcendental function. y' = y = 6e* x² +8 6(x²–2x+8)ex (x+8)²

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Q: #! Find f'cx) if fex)= Čx²+SX+2)(X-)

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Q: Find f-(-1,1) of the function: f(x, y) = x + xy +2a°y?

A: Let's find.

Q: Does the MVT apply to f(x) = - on the interval [1, 4]?

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Q: Show that the function f(x) = K. when xw0 when xois discontinuous at x = 0.

A: Solution

Q: 57. Is the function given by Sx + 1, for x 4, g(x) = continuous at x = 4? Why or why not?

A: gx=12x+1,   for  x<4-x+7,   for  x>4 Now left hand limit at x=4 is, limx→4-fx=limx→4-12x+1…

Q: differentiate the follouwing 243 a) f(x)=2x°-in/x|+3 arccos (X)

A: Since you have asked multiple questions in the same request, as per the policy, only the first…

Q: for x 2 - X Is differentiable at x = 2 but not at x = 1.

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Q: Find for the following function: 1- y = etan'x 2-x'y+ x*y 2 at x = 2

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Q: Assuming y cos (3xz) = 5 defines z as a function of x and y. Differentiate

A: we have to derivative

Q: Determine the extreme values of the function (exact coordinate(s) f(x) = 2sinx – x on the interval x…

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Q: Find a and b so that the function S4z - 3x² + 4, z -2 is both continuous and differentiable. a = b =

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Q: Compute the derivatives of the given functions. f(2) = In (7z²). 7a?). f'(x): / (z) = help…

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Q: 2. Let f(x) = r³, 0, if reQ if r ER\ {Q} Show that f'(0) = 0.

A: We have given a function ,  fx = x3 , x ∈ ℚ0 , x ∈ ℝ \ ℚ We need to show that , f'0 = 0 We know the…

Q: Find a function flx) such that f(x) -llex and %3D 3. f(0)-- 주

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Q: when that this 1x² + y² Shothathis sho (x, y) (0,0) and f(0,0) function is continous at (0,0)

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Q: Show that the function f(x) = exp(-|x|) is not differentiable at x = 0.

A: Given function is  fx=e-x given point is x=0.

Q: Suppose that f(x, y) = yVx³ + 1 on the domain D = {(x, y) | 0 < y <x < 3]

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Q: Obtain the first and second derivative of the following real-valued functions 1. ƒ : R → R, such…

A: Solution :1.fx=23x3-2xfirst derivative ,f'xf'x=29x2-2Second derivative…

Q: Suppose that f hits every value between y = 0 and y = 1 on the interval [0, 1]. Must f be continuous…

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Q: For what values of the constant c is the function f continuous on (-o, )? Show your work. S ex + 4,…

A: Please see the answer below

Q: 4. If f(x) = sin x, show that f(2.x) = 2f(x)f(-x) %3D

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Q: The function f(x) = 2 + 3x² – x³ is concave upward on the interval: (-∞, 1) (1, ∞0) (-∞, 0∞0) None

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Q: Obtain the MSE of f(x) = ex.

A: MSE = Maclaurin Series Expansion f(x)=ex formula f(x)=∑k=0∞f(k)(0)k!xk

Q: Q2 Evaluate whether the function 1-xy if xy # 1 z = x-y if xy = 1 continuous at (1,1) or not.

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Q: Show that the function xsin f(x)%D 0, When x 0 is continuous but not differenti able at x = 0 When x…

A: Let f be a function defined in the neighbourhood of 'a'. Then the function f is said to be…

Q: Find all the x-intercepts of f(x)=cos(x) on the interval [0,2π)

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Q: Find points of discontunity of the function,where k is real number 1 f(x, y) sin(4 – x2 – y?) - -

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Q: (b) Show that the function defined by √₂²+y f(x, y) = 0 if (x, y) = (0,0) is not differentiable at…

A: On solving this we will get

Q: Find the length of the curve defined as: f (x) = 5x from x = 0 to x = 1

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Q: Find the derivative of the fünction. y = 7(6 - x2)6 %3D

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Q: Find the values of a and b such that f is differentiable at x = 3

A: Given,            The function is fx=ax+bx≤32x1-1x&gt;3To find : Find the values of a and b such…

Q: Is the function F(x) as given is constant, increasing, or decreasing on the interval (0, ∞)?…

A: Fx=∫x2x1t dt⇒Fx=lntx2x⇒Fx=ln2x-lnx⇒Fx=ln2xx          ∵lnx-lny=lnxy⇒Fx=ln2

Q: 1 . Let f(r) 2r + 1

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Q: Suppose that a function f(x, y) satisfies fxx fyy – (fxy)² > 0 at a point (a, b). How is the sign of…

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Q: Find Tn cebtered at x=0 fir akk b for the function f(x) = 1/(1+x) at a=0

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