Suppose that the functions g and h are defined as follows. g (x) =x+2 h (x) = (x+5)(x- 5) 8 (a) Find h |(2). (b) Find all values that are NOT in the domain of h If there is more than one value, separate them with commas.

Q: If the functions f and g are continuous for all real x, is f + g always continuous for all real x?…

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Q: g(x, y) = In(2-x) 1-x2-y²

A: To find the domain of the function, g(x,y)=ln(2-x)1-x2-y2

Q: Consider the function f(x)=2x3+9x2−108x+5,  −6≤x≤4f(x)=2x3+9x2-108x+5,  -6≤x≤4. Use the derivatives…

A: Given, f(x)= 2x³+9x²-108x+5 -6<=x<=4

Q: Find the constant a such that the function is continuous on the entire real line. 7sin x if x < 0…

A: Here we find the value of constant a

Q: Discuss the continuity of the function on the closed interval.                              g(x) =…

A: We can not have a negative value under the square root.  So,

Q: Discuss the continuity of the function h(x) = }" (x2 + 7х -5, x3 – 2x2 + 1, x < 3 x 2 3 on the…

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Q: Suppose that f(x) = βx2 − 3     if x ≤ 2                                βx + 2       if x &gt; 2…

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Q: Is it possible to determine f (7) if f (x) = 3 for all x &lt; 7 and f is right-continuous at x = 7?…

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Q: If the function f (x) is continuous for all real numbers and if f (x) x²-4 when x + -2, then x+2 f…

A: f(-2) = -4

Q: Verify that f(x)=x3- 3x + 2 satisfies the hypotheses of the Mean Value Theorem on the interval…

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Q: Use intermediate value theorem to show that f(x) = -x3 + x2 + x + 1 must have at least one zero on…

A: Given: fx=-x3+x2+x+1 &amp; interval 0,2 To show: The given function must have at least one zero on…

Q: Discuss the continuity of the function on the closed interval.

A: Given: f(x)=x2-1x+1 The function is continuous at a point if the function returns a unique value…

Q: 19. Show that f(x) = x² + 1 is not one-to-one, using values of f (not the horizontal line test).

A: To show: The function fx=x2+1 is not one to one. Concept used: The function is one to one is and…

Q: Find the constant a, such that the function is continuous on the entire real line. f(x) = {2x2,…

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Q: Find all numbers C in the interval [− 2, 2] guaranteed by the Mean Value Theorem for the function…

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Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 2x3 – 6x² –…

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Q: Find and classify the extreme values of f(x)=6x^4 - 4x^6 over the interval [-2,2]

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Q: Find the intervals on which the function f(x) =x2 +5x2 -8x+1 is strictly increasing function

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Q: how that the function  f(x)=x3-3x2+3x-100 is increasing on R

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Q: x -4x +5 - Prove that: f' x x-2

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Find

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Q: Discuss the continuity of the function f(x) = {x2 − 3x if x &lt; 2 2x + 4 if x ≥ 2 on the open…

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Q: Find the constant a such that the function is continuous on the entire real line. 8sin x if x < 0…

A: For continuity of f(x) LHL=RHL     so find lhl and rhl and equate both to get a.

Q: Find the constant a such that the function is continuous on the entire real line. 1 = √7x², lax - 5,…

A: Topic = Function

Q: Find the constant a such that the function is continuous on the entire real line. 8sin x If x < 0 if…

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Q: Suppose that 2 ≤ f '(x) ≤ 3 for all values of x. What are the minimum and maximum possible values of…

A: Given , Suppose that 2 &lt;= f’ (x) &lt;= 3 for all values of x. The minimum and maximum possible…

Q: explain why the function has at least one zero in the given interval. f(x) = x^3+ 5x-3 intervals…

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Q: Find a zero of f(x)=x-x³ by finding a fixed point of x= g(x)=x³.

A: we have to find the fixed point of g(x)

Q: Find the constant a such that the function is continuous on the entire real line. 8sin x if x < 0…

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Q: Verify the mean value theorem for the function f(x) =(x²- 3x)(x+2) over the interval -3, 3]

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Q: Check the continuity of the function f(x) at x = -2 f(x) = - 6r + 3x l-6x if xs-2 if x>-2

A: Given,         The function fx at x=-2.           fx=x2+3xif x≤-2x3-6xif x&gt;-2

Q: Suppose that f(x) = βx2-3     if x≤2                                   βx+2       if x &gt; 2…

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Q: If f(x)<0 for all real numbers x, then f is decreasing on(-♾,♾) True or false

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Q: Show whether f(x) is continuous (3х-2 f(x)={ x-2 x² -4 for x=- for x+ -

A: Given that, f(x) = 3x - 2; for x = - 2 f(x) = (x + 2)/(x^2 - 4); for x not equal to - 2 So when x is…

Q: Discuss the continuity of the function g(x) = 1/(x^2-4) on the interval (0, 2] and [−1, 3].

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Q: Discuss the continuity of the function f(x) = {x2 − 3x if x &lt; 22x + 4 if x ≥ 2on the closed…

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Q: Discuss the continuity of the function f(x) = {x^2 - 3x         if x &lt; 2           {2x + 4…

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Q: Find a function for which f'(x) exists for all real numbers but f"(x) doesn't exist for all real…

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Q: Show that the function g(x)  =x| x has an inflection pointat (0, 0) but g"(0) does not exist

A: Given: The function g(x)= x |x| For x&lt;0, |x|=-x, thus g(x)=x(-x)=-x2 Also for x≥0, |x|=x, thus…

Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 6x3 - 9x² –…

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Q: Find all critical points of the function f(x) = x³ + 3x² them in descending order and separate them…

A: Find all critical points of the function f(x) = x³ + 3x² - 5x + 9.

Q: Suppose that 4 ≤ f '(x) ≤ 5 for all values of x. What are the minimum and maximum possible values of…

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Q: If f is differentiable and f'(x)=x³-2x²-x+2, then fis increasing or

A: Given, x³−2x²−x+2=f' We equate the given function to zero for critical points. x³−2x²−x+2=0   Step…

Q: If f : [0, 3] → R is continuous, must its range be a closed interval?  use the continuous map

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Q: The domain of function x) = In(2– x) is %3D

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Q: find the domains of ƒ, g, ƒ + g, and ƒ . g ƒ(x) = x, g(x) = √x - 1

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Q: Identify the removable discontinuity. f(x) =  x3 + 2x2  over  x + 2

A: Given query is to find identify the removable discontinuity.

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.