Determine the values of a and b such that the function (x -a ,x <-1 f (x )={2x +1 ,-11 Is continuous of all values of x.

Q: Find c such that the function x2 – 9 x с is continuous everywhere. - С —

A: f(x) will be continuous at x=c. when value of the function at c , left hand limit of f(x) at c  and…

Q: Determine the values of a, b, and c so that the function (sin(a + 1)x + sin x x0 is continuous for…

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Q: Find the absolute maximum and absolute minimum values of f on the given interval. a)…

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Q: Sketch the graph of a continuous function y = h(x) such that a. h(0) = 0, -2 < h(x) < 2 for all x,…

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Q: Let ƒ(x), g(x) be two continuously differentiable functions satisfying the relationships ƒ′(x) =…

A: Given,

Q: Let f(x) be a continuous function defined on the interval 2 < x < xo such that f(4) : 14 - |f(x)| <…

A: From the formula we can eausly do these type of questions. I will the fomula and questions in detail…

Q: Let f [0, 2] → R be a continuous function, with ƒ(0) ≤ f(1) ≤ f(2). Show that there : exists xo [0,…

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Q: Find the constant a such that the function is continuous on the entire real line. x 21 f(x) = lax –…

A: The function is continuous on the entire real line. We have to find the value of a.

Q: Determine the set of points at which the function is continuous. a) f(x,y) = ln (x² + y² – 4)

A: According to question given thatf(x,y)=ln (x2+y2-4)

Q: Consider the piecewise function: |x- 1| x² – 1' x <1 f(x) = (Ax² + 6, x 2 1 For what real number A…

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Q: Assume that the function f is such that f(3) = 1, ſ f(x) dx = 5, and f'(x) is continuous on [0, 3].…

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Q: a continuous function f such that f(4) = 4, f'(4) = 0, ƒ'"(x) 4 is:

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Q: Let I be an interval disjointed from {-1, 1} . Prove that the function f(x) = x + (1/x) is…

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Q: Find the constant a such that the function is continuous on the entire real number line. S x + 5, x…

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Q: Determine if the function f(x)= are uniform X continuous on the interval I= [0,1]

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Q: Find all values of c such that f is continuous on (-0, 0). 1- x2, f(z) = { – x², x. C = (smaller…

A: Given function is, fx=1-x2   , x≤cx          ,x&gt;c  Since 1-x2 and x are continuous on the…

Q: Consider two continuous functions f(x) and g(x) along with two real numbers a and b where a < b. If…

A: Two continuous function fx and gx Let fx=aconstant, constant function is always continuous. gx=ax,…

Q: (b) A function f(x) continuous at 0 and g(x) not continuous at 0 such that f(x)+g(x) is continuous…

A: A function fx is continuous at  x=a, if limx→a+f(x)  = limx→a-f(x) = f(a)

Q: Find the constant a such that the function is continuous on the entire real line. (5x2, ах — 3, x 2…

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Q: Find all values of c such that f is continuous on (-00, 00). f(r) = { 8 – x², !! x>c

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Q: Find all values of "c" such that the function f(x) is continuous over  ( − ∞ , ∞ ) f(x) = 1 - x^2…

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Q: Is the function continuous  f(x) = e^x / 1 - e^x

A: We need to check the continuity of the function

Q: Sketch the graph of a continuous function y = h(x) such that a. h(0) = 0,–2 < h(x) < 2 for all x,…

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Q: Let f(x) = CX– 2, x > I lx+ 8, x < 1 For what value of c is f(x) continuous on (-00, 0)

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Q: Consider a function f(x) = |x – 3|. a. Show that f (x) is not differentiable at 3. -

A: Given         f(x) =|x-3|

Q: For what value of a is x² -1, x< 3 f(x) 2ax, x2 3 continuous at every x?

A: Given function is Since, f(x) is continuous at every x, so f(x) is continuous at x=3.

Q: 1 If f(x) is a non-negative continuous function for all x, such that f(x) + + f(x+1/2) = 1,0 ≤ x ≤ -…

A: Given that fx is a non-negative continuous function for all x, such that fx+fx+12 = 1 for 0 ≤ x ≤…

Q: Find the value of a such that the function S(«) = {** -1, x < 3 x 2 3 | f(x) = 2ах, is continuous at…

A: Given:      f(x) = x2 - 1  , x &lt; 3     f(x) = 2ax  ,   x ≥ 3

Q: Find all values of the constant a such that f is continuous for all real numbers.

A: Given function is Since f(x) is continuous for all real numbers , so f(x) is continuous at x=0.…

Q: Find values of the constants k and m, if possible, that will make the function f continuous…

A: If f is continuous at x=a then limx→a-fx=limx→a+fx=fa . Assume , f is continuous every where to find…

Q: g(x) = sec(x) %3D

A: To find all the intervals the function g(x)=sec(x) is continuous

Q: Find a value of k making h(x) continuous on [0, 5]. kx , 0 < x < 1 h(x) = x +3, 1<x < 5

A: Given: hx=kx,0≤x&lt;1x+3,1≤x≤5 given function will be continuous over 0,5, if it will be continuous…

Q: Let f(x) = x-*,x > 0. Find the interval on which f is increasing or decreasing and find the local…

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Q: Determine the set of points at which the function is continuous. F(x, y) - х-у 1 + x² + y2

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Q: Q2/ (a):Find the points at which the function f is continuous and the points at which ƒ is not…

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Q: Find all values of the constant a such that f is continuous for all real numbers. ах x 2 0 f(x): tan…

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Q: Determine the value of c such that the function is continuous on the entire line. f(x) = {* + 3, xs2…

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Q: Find the constant a such that the function is continuous on the entire rea 6sin x X g(x) = a 8x if x…

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Q: Prove that the function f(x) = cos x is strictly decreasing on the interval [0,1]. %3!

A: 5) Given that, fx=cosx

Q: Find a value of k making h(x) continuous on [0, 5]. 0 <x < 2 x +1, 2<x < 5 eka, h(x)

A: Givenh(x)=ekx    0≤x&lt;2          x+1  2≤x≤5To find a value k when h is continuous on…

Q: Determine if g (x) = is continuous at x = 0

A: A function f(x) is continuous at x=a if, limx→af(x)=f(a). We try to evaluate limx→04-xx and f(0) and…

Q: If f is a continuous function and F'(x)=f(x) for all x € R, then - x)dx=?

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Q: (c) A function f(x) continuous at 0 and g(x) not continuous at 0 such that f(x)g(x) is continuous at…

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Q: 7. Find the intervals on which the function is continuous, J (X) = +3)2+6

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Q: Determine the set of points at which the function is continuous. a) f(x,y) = ln (a²² + y² – 4)

A: Given function is                                                              f(x, y)=ln(x2+y2-4)…

Q: x 2

A: Consider the function f(x)=x-1              ,       x≤02x2-3x+1    ,       0&lt;x≤23x3-x2          ,…

Q: Let I be an interval disjointed from (-1,1) Prove that the function f(x) = x + (1/x) is increasing…

A: Solution: Consider the given function is: f(x) = x + 1x    ...(1) Also, the given interval Let I is…

Q: Determine unknown constants a and b for which g(x) is continuous at x=1. [5x - 2 x 1

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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.