y = the absolute value of x2 - 81 a.) Describe the x-values at which the function is differentiable using interval notation.

Q: determine intervals in which solutions are sure to exist. 3. (x − 1) y(4) + (x + 1) y″ + (tan x) y =…

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Q: Identify the open intervals on which the function is increasing or decreasing. (Enter your answers…

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Q: Where is f(x)= x³ differentiable? (interval)

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A: For maximum or minimum consider f'(x)=0

Q: a. Find the absolute extrema of flx) = x2 – 3x + 3 on the interval

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A: a rational function f(x)=p(x)q(x)   is discontinuous at point wheher q(x)=0

Q: Consider the function f (x) = -7x² – 14x – 6 on the interval [-3, 2]. Find the absolute extrema for…

A: Given: f(x)=-7x^2-14x-6 Interval: [-3,2]

Q: Find the domain of the function. (Enter your answer using interval notation.) h(x) = In(x) + In(6 –…

A: The function is given by hx = lnx+ln6-x To evaluate : The domain of the function.

Q: the interval of differencing being unity. Ex Evaluate

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Q: At what points is the function y=(x+1)/(x^2-3x+2) continuous? Describe the set of x-values where…

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Q: Find the absolute extrema of f(x)=x/(9-x) on the interval[5,9]

A: fx=x9-x  ,  5, 9 Differentiating with respect to x, we get f/x=dxdx·9-x+d9-xdx·x…

Q: Consider the following function. y = x2  divided by x2 - 36 a.) Describe the x-values at which the…

A: Given:y=x2x2-36To find:The x-values at which the function is differentiable using interval notation.…

Q: Find the functions and their domains. (Enter the domains in interval notation.) f(x) = 9x + 8,…

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Q: Describe the x-values at which f is differentiable. (Enter your answer using interval notation.)…

A: The given function is (x-1)25. We have to find out the value of x, where the given function is not…

Q: Let the function f be defined by the equation y = f(x), where x and f(x) are real numbers. Find the…

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Q: Verify that the Intermediate Value theorem

A: Concept: Intermediate value theorem is precise mathematical statement having the properties of…

Q: sketch the interval (a, b) on the x-axiswith the point c inside. Then find a value of δ> 0 such…

A: -72<x<-120<x+3<sLet fx=x+3

Q: In which interval, function f(x)=x3e-x is increasing and concave up? (0, 3(sqrt3)) (3-sqrt3, 3) (3,…

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Q: Use a graphing utility to graph the function and find the absolute extren not exist, enter DNE.)…

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Q: Describe the x-values at which f is differentiable. (Enter your answer using interval notation.) Sx²…

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Q: Express the set of numbers x satisfying the given condition as an interval.        I x -4 I < 2

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Q: 1.Use interval notation to determine f(x)

A: Concept: The graph of a function: The graph of a function is the set of all points (x,y) in the…

Q: Find the domain of the function. (Enter your answer using interval notation.) h(x) = In(x) + In(5 –…

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Q: Describe the interval(s) on which the function is continuous. (Enter your answer using interval…

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Q: Identify any x-values at which the absolute value function f(x)=5|x+8|, is   not differentiable:…

A: Given: fx=5x+8

Q: Determine the point(s) at which the given function f(x) is continuous. 9 f(x) = , 7x х-2 Describe…

A: Given, f(x)=9x-2-7x

Q: Let f(x) Determine the intervals on which f'(x) > 0 and f'(x) 0

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Q: ind the absolute extrema of the​ function, if they​ exist, over the indicated interval. Also…

A: Given function is  fx=x9=x1/9 and interval [-1, 0]

Q: Describe the situation in which the distance that point x is from 10 is at least 15 units. Express…

A: Distance of x from 10 = Now, distance of point x from 10 is at least 15 units. So,

Q: Determine the point(s) at which the given function f(x) is continuous. f(x) = /5x+ 15 Describe the…

A: Rule: A function f(x)=x is said to be continuous when x≥0.

Q: Describe the x-values at which f is differentiable. (Enter your answer using interval notation.)…

A: F(X)=(X-4)2/5 F(x =2/5 (x-4)2/5-1

Q: Find the domain of the function. h(x) = Inx+In(2-x). Express your answer in interval notation.

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: Consider the function f (x) = 4x³ – 30x² + 48x on the interval [-3, 7]. Find the absolute extrema…

A: Given ,  f(x) = 4x3 - 30x2 + 48x on the interval [-3 , 7] We have to find the absolute extrema for…

Q: Determine the open intervals on which the graph s concave upward or concave downward. (Enter your…

A: Solved below

Q: 81. f(x) = |x – 5|

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Q: Without solving completely, explain why the function x? + 5x [0, 1]. Give an informal description of…

A: For a function: y=f(x), the dependent variable is y and the independent variable is x. The value of…

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Q: Describe the interval(s) on which the function is continuous. (Enter your answer using interval…

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Q: Describe the x-values at which f is differentiable x² - 5, f(x) 15-x, 2' 5 – x, x > 0

A: When x≤0 fx=x2-5 Left-Hand Limit  = limx→0x2-5=-5

Q: Express the set W = {r|x < 2} using interval notation. %3D

A: W={x | x&lt;=2}

Q: Identify the open intervals on which the function is increasing or decreasing. (Enter your answers…

A: If f'(x)&gt;0 for every x on some interval I , then f(x) is increasing function . If f'(x)&lt;0 for…

Q: Determine the interval(s) for which f(x) ≥ 0. (Enter your answer using interval notation. Enter…

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Q: Find the number that satisfies the conclusion of theMean Value Theorem on the given interval. Graph…

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Q: Verify that the Intermediate Value Theorem applies to the indicated interval and find the value of c…

A: f(x) =x2+x+1        [0,7] f(c) = 7

Q: sketch the interval (a, b) on the x-axiswith the point c inside. Then find a value of δ&gt; 0 such…

A: Now, we want to find the value of δ such that a &lt; x &lt; b whenever 0 &lt; | x - c | &lt; δ.…

Q: (-x? - 2х, х и -2 2) f(x) = (1, x = -2

A: Given:  fx=-x2-2x,  x≠-21,             x=-2 To Find: The intervals on which the given function is…

Q: y = xV 100 – x² increasing decreasing

A: The function is given as , y=x100-x2 find open intervals on which the function is increasing or…

Q: (a) Find a number x in the closed interval , such that the sum of the number and its reciprocal is…

A: A continuous function f on a closed interval a,b has both absolute maximum (largest ) and absolute…

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.