48. Continuous Function Find a value for a so that the function | 2x + 3, xs 2 f(x) ax + 1, x>2 is continuouS

Q: 3.The absolute maximum and minimum values of f(x)=−(x^2+x)^2/3 over the interval [-3, 4]. absolute…

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Q: 7. Derivative of the Reciprocal Use the limit definition to prove f'(x) 5²(x) d 7. dx (f(x), Hint:…

A: To prove that: The derivative of a function is given by in terms of limit h tends to zero is given…

Q: lim f(x) = c lim f(x) = 00 lim f(x) = 0+ lim f(x) = 0- x-1+ X-1- f(0) = 0,f(-1) = -f(-2) = -

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Q: 3. A function f(x) satisfies the inequality 1-<f(x) < 1 + tan²x, when x →0. Using the Sandwich…

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Q: Consider the function f(x)=4 sin x+x2+5x –10 with domain the closed interval [0, 27]. (a) Show that…

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Q: lim [f(x)]" = [ lim f(x)]" where n is a positive integer [x→a

A: Given: To provelimx→a f(x)n=limx→af(x)n where  n is a positive integer.

Q: Find all critical values for f(x) = (x + 9)' (x + 1)°. The critical values occur at x = (Enter your…

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Q: Continuous extension Find a value of c that makes the function 9x - 3 sin 3x 5x x + 0 f(x) = x = 0…

A: is continuous at x=0 We need to find the value of c.

Q: Shade the region under the graph of f(x)= 2/e^x bounded by x= -1 and x= 2 . Find the area of the…

A: The given function y=f(x)=2ex is bounded by x=-1 and x=2. The area of the bounded region is given by…

Q: 1. Find the open intervals where the function is increasing and the intervals where the function is…

A: We are going to find the interval

Q: 59. Derivative of the Reciprocal Use the limit definition to prove f'(x) dx f(x) f²(x) Hint: Show…

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Q: V. Consider the function f that is continuous everywhere except at x = 0 and whose only intercept is…

A: The graph of given condition is as below

Q: 7. (Graphically -Vertical Tangent Line!) The function f (x) = x1/3 is continuous at x = 0, however…

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Q: Using the First Derivative Test Consider the function         ƒ(x) = 3x4 - 4x3 - 6x2 + 12x + 1.a.…

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Q: What’s the absolute maximum and minimum for x + 1/x

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Q: (a) Give an example of a function f(x) such that lim,0- f(x) = 2, lim0+ f(x) = 3, and f(0) = 1…

A: Important key points :   An ordinary partial ddifferential equation , the dependentvariable and its…

Q: 2 -6 -4 2 6 4.

A: given

Q: 4. Find the intervals where the function is increasing and decreasing. Use this information to…

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Q: f(x) = 2xe^-5x^2 , x does not equal 0 Find critical points in increasing order and apply the Second…

A: f(x)=2xe-5x2 To find out critical points we take first derivative and set it equal to 0 then we…

Q: Determine the value of the constant a for which the tunction f(X) Is 2 x +7x+ 12 if x# - 4 f(x) =…

A: We have been given the function f(x) which is continuous at x = -4 and we have to find the value of…

Q: 8. Rolle's Theorem does not apply to the function f (x) = (x+1)2 on the interval [-2, 0]. Explain…

A: Given that:                           f(x) = 2x+12   To Check: Rolle's theorem in the interval [-2,…

Q: IV. Exercišēs Determine if the following functions are continuous at the given value of x. 3. f(x) =…

A: check the value of function for finding whether its continuous or not.

Q: An unknown constant Determine the value of the constant a for which the function x + 3x + 2 ifx + -1…

A: Given: f(x)=x2+3x+2x+1if x≠-1          aif x=-1 To determine: Value of the constant a for which the…

Q: Find the absolute maximum and minimum of the function on the given interval. a) f(x) = 4x/ x^2 + 4…

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Q: a. Use the Intermediate Value Theorem to show that the following equation has a solution on the…

A: According to Intermediate Value Theorem, if a function is continuous on an interval, then, function…

Q: Two functions f(x) and g(x), are continuous and differentiable for all real numbers. Some values of…

A: The function of function is defined when the variables in one function are replaced by another…

Q: Find the area (in square units) of the region under the graph of the function f on the interval [1,…

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Q: Example Let f(x) = /x. 1. Find f (x) using the (limit) definition. 2. Find f'(4). 3. Find the…

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Q: Describe all functions y=f(x) which are defined for all x∈R and satisfy the equation f(x)= 1/f(x)

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Q: Find f(x) where we cannot solve for f'(x) = 0, but f(x) cannot be = 1/x

A: Division rule of derivatives: uv'=vu'-uv'v2  Let us take f(x)=1x2 Solve for f'(x)=0

Q: 10 +x Find the absolute extrema of the function f(x) = on the interval [5,8]. %3! 10 - X

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Q: etermine the intervals where the function f(x) = x 2 e −x is increasing and where it is decreasing

A: Determine the intervals where the function f(x) = x 2 e −x is increasing and where it is…

Q: 15. Domain (x : x 2 0}: ƒ-'(x) = Vi - x² ; domain {x : x < 0}: f-'(x) = - y=f-(x) 1.5 y=f(x) 0.5 2

A: Consider the given function f-1x=1-x2x So, the function f-1x is defined if  x≠0  and 1-x2≥0⇒x2≤1⇒x∈[…

Q: Mean Value Theorem. So I determined that this is continuous and differentiable at [1,7]. I just do…

A: Given function is  fx=1x

Q: sin x + 2 What is the domain of f(x) = and where isf continuous? %3D X-8 The domain of f(x) is…

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Q: Electric Current. Suppose you have two electronic devices that have different currents when x = 2.…

A: The given function,   f(x)=a+3x+2x2if x&lt;24x2+6x+8if x≥2

Q: C. Find the values of the constants c and k that make the function continuous at every number. [3x…

A: Given Fx=3x+7   if   x≤4kx-1   if   4&lt;x The objective is to find the value of k.

Q: lim f(x) where f(x) = - r-3 ,x 3

A: We have to find out the limit

Q: (kax if x<2 f(x)=11- kx if 2s x Consider the piecewise function: 6. Find values of the constants a…

A: The given function is,

Q: f(x) = 4x(square root of 3x^2 + 3) a) find all critical values of f. Use interval notation to…

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Q: (4) Let f(x) = Vx² + 1 +x. %3D Consider the function g(x) = f(x+3) – f(x) with domain the set of…

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Q: Graph of f(x) Graph of / A 1. In the interval 0<x< 1 of the first derivative test, f(x) is Ⓒa.…

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Q: За? — 6х + 7 - g(x) x2 + x + 1

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Q: X-2 What can we conclude about the function f(x) = %3D X-3 O The function is discontinuous at X = 3.…

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Q: absolute minimum value of the function f(x) =4x² – 8x+1 over the interval (0,5 -3 4 2 III

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Q: (2, r+1, x+x-2 x-1 f (x) = k, x = 1, Find the value of k so that f (x) is a continuous function for…

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Q: lim x → 0− g(x)   lim x → 0+ g(x) Is g continuous at x = 0?

A: On the left side of x=0, y is approaching -3 So, limit x-&gt; 0^- g(x)= - 3

Q: 6-x Find the absolute extrema if they exist, as well as all values of x where they occur, for the…

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