f(x)=- %3D x² +6x+9

Q: Find the value k that makes the function continuous. (ka?, x > -2 f (x) kx + 18, x < -2

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Q: Determine the value for k that will make the function continuous at c = 4. x² – 9 if x 4

A: Left-handed limit of a function at a point is obtained by approaching the point from the left on the…

Q: Given the function h (x) = -v2 – x, what is h (x)?

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Q: Find numbers a and b, or k, so that f is continuous at every point. 3x+ 9, if x<-6 f(x) = { kx+ 6,…

A: Hair we are given that the function is continuous at every point. we use the concept of limit for…

Q: Find the values of x for which the function is continuous. - 7 f (x) = 2 + 84

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Q: Find the intervals on which the function y=xx(x&gt;0) is increasing and decreasing.

A: We take ln on both sides of the function

Q: Find the intervals where f(x) = x2e−x is increasing and where it is decreasing.

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Q: Find the intervals on which the function is continuous. x +5 17) y =2-7x + 10

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Q: f(x)% = x- 3x3 + 2x2-5x-7 at x = -1 %3D vnaud

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Q: Find the absolute extrema of the function on the closed interval.

A: Find the derivative for g(x).…

Q: Find the value of the constant bl that makes the following function continuous on (-∞, ∞). if x 6|…

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Q: Locate the discontinuities of the function. 2 f(x) = 1 + e7/x

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Q: f(x) = x2 -4x-2 at x = 1 %3D %3D

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Q: Find the value of the constant (a, b, or c) that makes the function continuous.

A: A function fx is continuous at x=a if its left-hand limit, right-hand limit, and fa are equal and…

Q: Q1: - Find C that make the function f(x) continuous f(x) = {| x +3 Сх+ 6 x 2

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Q: Find the value of the constant (a , b, or c) that makes the function continuous.

A: the given function is: fx=x2-c          for x&lt;54x+2c      for x≥5 we have to find the value of c…

Q: Graph the function f(x) = 4 − x and determine the interval(s) for which f(x) ≥ 0.

A: Given, fx=4-x To graph f(x) and determine the interval(s) for which f(x) ≥ 0.

Q: Find the graph of the function f(x) = [x] + [x/2] from R to R.

A: Given function is fx=x+x2. Definition: Floor function is the greatest integer that is less than or…

Q: At what interval of x will the function continuous, f(x) = { 3x²-x-2 x-1 0, x= 1 ", x#1

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Q: f(x) at x = - 3 X-3

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Q: Find the constant a such that the function is continuous on the entire real line. 9x², ax - 3, a = x…

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Q: Find the value of the constant & that makes the following function continuous on (-o, o). | 2x – 6…

A: fx=2x-6     if  x≤6-3x+b  if  x&gt;6 Since the function is a polynomial function for all x&lt;6…

Q: Is the function below continuous at x = -5? f(x)=x3−2x2+5x+1

A: We are to simplify

Q: Find the interval where the function, f(x) = 5 V3x – 2V3x + 57 is increasing?

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Q: 2. Use the graph of the function f(x) to estimate where (a) f'(x)= 0, y f(x) (b) f'(x) 0.

A: (a) f'(x) =0   =&gt; the slope is zero, it means when the graph is parallel to x-axis  i.e. at…

Q: What is the value "L", if exists, when a variable "x" in f(x) approaches a certain number "d" in the…

A: Given: A function fx is given. To Find: What is the value "L", if exists, when a variable "x" in…

Q: Find the value of k, if the constant k that makes the function continuous:

A: Given,          f(x)=x2+k2if x≤4kx+12if x&gt;4

Q: Determine the possible pairs of values (a,b) which make the function below continuous everywhere.…

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Q: Find the length of the are of the function x² = 4y from x = -3 to x = 3.

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Q: Find a value for the constant k, if possible, that will make the function continuous. Skx², (2x + k,…

A: Answer: The solution is as given below:

Q: On what domain is the function f(x)=x^2+7x−6 continuous?

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Q: : Find the value of k that makes function continuous at x = 5 5x? – k x 5 f(x) =

A: Limit of a function at a point exists if the left-handed limit and right-handed limits at that point…

Q: Find the local extrema of the function f(x)=x3−12x.

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Q: Find the value for k so that the function will be continuous at x = 2. 4x + 16 if x 2

A: The function fx is continuous at x=a, if limx→a-fx=limx→a+fx It is given that fx=4x+16if…

Q: Find the constant a, or the constants a and b, such that the function is continuous on the entire…

A: Given function is: fx=3x3,x≤1ax+5,x&gt;1 We know that a function is continuous at any point x=c if,…

Q: Find the areas below. a) Between the graph of f(x) = 50 + 3x² and x-axis over the interval [-2, 4].

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Q: Find the domain of the function in interval notation: f(x) = V + 17 %3D

A: Domain is the set of x values for which the function is defined We know that square root (negative…

Q: Explain if the function is continuous or not for the given number a. if x>1 if x = 1 ,a=1 if x<1…

A: we have given function     we need to determine the continuity at a=1

Q: Find values of the constants a and b, that make the function f(x) continuous everywhere. 2x3 + x +…

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Q: Find a value of the constant k, if possible, that will make the function continuous everywhere. (kx…

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Q: Find the absolute extrema of the function on the closed interval. F(x) = x³ -?, (-1, 4] 2

A: Given,            fx=x3-32x2 , -1,4To find : Find the absolute extrema of the function on the closed…

Q: Find the values that make the piecewise function continuous: 2, XS-1 f(x) = ax + b, -1<x< 3 x2 3 -2,

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Q: Find the lineearization L(x) of the function f(x) = x^3/4 at x = 16.

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Q: Determine whether the following function is continuous at the given point r = 3x2 + 17x -6 1 f(x) =…

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Q: Determine the possible pairs of values (a, b) which make the function below continuous everywhere.…

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Q: Find the constant a such that the function is continuous on the entire real line. 5x², ах — 7, f(x)…

A: For a function to be continuous, the value of the left and right limits at critical point needs to…

Q: Find the open intervals on which the function is increasing y = x/100 – x²

A: A function is said to be increasing in an interval its derivative is positive in that interval.

Q: Find the constant a such that the function is continuous on the entire real number line. Sx³, x 2…

A: Given : f(x) = x3,x≤2ax2,x&gt;2 and the function is continuous. To find : value of a?

Q: Find the absolute extrema of the function f(x) = x³ 23-a on the interval

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Q: Find the intervals on which the function f(x)=xlnx is increasing and decreasing.

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.