Show that the function f(x) = x' + 3x² is continuous at every real number a.

Q: Compute the derivative f'(x) for f(x) = log(x*) sin(x³).

A: Topic - derivative

Q: Determine the derivative of f(x) = 3 x2 In x with respect to x. f '(x) :

A: We differentiate both sides with respect to x and apply the rule d/dx(uv)=ud/dx(v)+vd/dx(u)

Q: Use the second order derivative test to find local exterma of the function  f(x) =x3-9x2-48x+72 on…

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Q: Determine if the function f(x)= is continuous -- sin(x) x on the interval I= (0,1).

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. x. 4 g(x)…

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Q: ,x 1 Is the function k(x) = {x²-1 2,x = 1 continuous at x = 1?

A: We use L' hospital rule to find the limit.

Q: Find the hundredth derivative of the function f (x) = cos(2x). O f(100) (x) = -2!00 cos(2x) O f(100)…

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Q: Determine the derivative of f(x) = 3 x² In x with respect to x. f'(x) = |

A: We have to find f'(x)

Q: Show that the function is continuous. (x) = 3x cos 3x

A: Show that the function is continuous. (x) = 3x cos 3x

Q: п-(х-4)" 22и. (2n — 1) Ax) =En=0 n:

A: Solution of given problem as follow

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: Determine the derivative of f(x) = ( In x )6 with respect to x. f'(x) =

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Q: Let f be a continuous function with f'(x) = 3x² Of has no relative maxima. 0x=0 0x=2 0x=1 - 6x. At…

A: f be a continuous function with f'x=3x2-6x

Q: The function f(x)=(2-x)/(3) is continuous at

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Q: If the function is defined y=2x when x=3, is this function differentiable at x=3? Also, is this…

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. h(x) = 2…

A: solution is given below

Q: Prove that f (x) = x3 − 12x is differentiable. Compute f'(x) and findan equation of the tangent line…

A: For a function f(x) to be differentiable the limit limh→0f(x+h)-f(x)h must exist. This limit is…

Q: Suppose that f(x) is a continuous function on the interval [0, π]. If f(x)=(sin x)² for 0<x<, then…

A: Since the f(x) is continuous function in [0, π], therefore the value of function at x = 0 must equal…

Q: Show that the function is continuous on  (∞ , -∞).

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Q: Explain why the function ƒ(x) = sin (1/x) has no continuous extension to x = 0

A: Then we can extend the definition of the function at that point to make it continuous there.

Q: Prove that constant function is differentiable at ever x ER.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 16. Show that f(x) = Vx - 2 is continuous at x=2 but not differentiable at x=2.

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Q: Show that f(x) = x – cos(x) has only 1 real zero on the interval [0, .

A: given fx=x-cosxx∈0,π2

Q: 4. In f(x) = {1– x² if -1sxs 1. Is the function continuous at x=1? Prove. (x² – 1 if x > 1

A: Given Function:                  f(x)={x2-1, if x&lt;-11-x2 if -1≤x≤1x2-1  if x&gt;1    To…

Q: b) Use the definition of the derivative to compute f'(x) for 1)f(x) = 2v-5x + 9, 2)f(x) = x sin 3x…

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Q: 10. Show that f (x) = { x² sin(1/x) if x + 0 if x is differentiable, but the derivative is not…

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Q: Where is Log(z2 + 2) holomorphic (Analytic ) function ?

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Q: Determine where the function F(x)=8x/x2+4 is continuous. The function is continuous on ?

A: Suppose   are continuous function at then rational function is continuous at   if .

Q: How must f(0) be determined so that the function f(x) = x2-x ニー x0, is continuous x-1 at X= 0?

A: Let f be a real function . Let a be any point in its domain . If limx→afx exist and equal to fa Then…

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.

A: To find the derivative of the h(x) using fundamental theorem of calculus part 1.

Q: Let f'(x) = 100x(2x+3)(x-5), use the first derivative test to determine the location of the local…

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Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of f(2) = | : 1 -dt 1 + t5…

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Q: Find the value of K that make the function f continuous at x=2 -4 スー3x+2 sin(nx) + kx + k if x 2

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Q: Find the derivative of f (x) = arcsin (x²). 2x f' (x) = 1-a4 f' (x) V1-x4 2x O f' (x) = V1-a² O f'…

A: Use differentiation of trigonometric function

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: Find the hundredth derivative of the function f (x) = cos(2x) . O f(100) (x) = -2100 cos(2x) O…

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Q: Use the first derivatives test to find the local exterma of f(x) =x3-12x on R

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Q: Use the second derivative test to find the local exterma of the function f(x) =x3+12x2-5 on R

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Q: : Find the value of k that makes function continuous at x = 4 %3D 3x + 6 x > 4 f(x) = 6x – k x < 4 -

A: To find: The value of k

Q: 4. Show that the function is continuous on (-00, 0). f(2) = {0 x* sin(1/x) if x 01 if x = 0 S

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Q: Compute the derivative of f(1) = In(x In(x² In(r³))).

A: The given function f(x)=lnx lnx2 lnx3

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: consider a continuous function y=f(x) whose first derivative is y'=x(x- 2).

A: We can find the interval as below.

Q: Let [x² + 1 _ if x 1 f(x) - Is f differentiable at 1?:

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Q: Find the derivative of the transcendental function. h(x) = 7e cos x h'(x) = %3D

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Q: Use the First Fundamental Theorem of Calculus to find F"(x) if = [*_ sinh√/1 +ť² dt. F(x) =

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