For what value of the constant c is the function f continuous on (-o S cx2 + 8x x3 – cx if x < 3 f(x) if x > 3 с 3

Q: 5. Show that the function h(x, y) defined by if r2 + y? 1 is discontinuous.

A:

Q: For what value of the constant c is the function f continuous on (−∞, ∞)? f(x) =    cx2 + 6x…

A: fx=cx2+6x     if x&lt;3x3-cx       if x≥3 fx is continuous for all x&lt;3 &amp; x&gt;3, because it…

Q: What is the value of k so that the function f(x) is continuous at x=2 O-3 O - 3/2 1/2 0 1 T-2k f(x)…

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Q: For what value of the constant c is the function f continuous on (−∞, ∞)? f(x) =      cx2…

A: The function f is defined by: The definition of the function changes at x=5So the function is said…

Q: If f(x) is continuous on (-15,-5)such that, -10 SI5 f(x)dx=13 and/" f(x)dx =6 then find f(x)dx -10…

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Q: For what values of a and b will f(x) be continuous on everywhere at x = 2 if the function is x² – 4…

A: f(x)=x2-4x-2x&lt;2ax2-bx+32≤x&lt;32x-a+bx≥3

Q: f(x) dx = 4, Suppose f(x) dx = 3, g(x) dx = 2. Which, if any, of the following statements are true?…

A: Given:

Q: 9. If f(5) = 10, f ' is continuous, and f '(x) dx = 15 18, what is the value of f(6)? %3D f(6) =

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Q: For what value of b, f(x) is continuous at every x? (a²x-2a f(x) = (12 x2 2 x< 2

A: As f(x) has two parts and both parts are continuous in given x so make continuous only at point x= 2

Q: on f(x, y) = 3x + 9y subject to th %3D

A:

Q: 5. Find the most general antiderivative of the following function. 2x² +5 f(x) = x² +1

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Q: For what values of a and b is -2, f(x) = { ax – b, -1 <x< 1 3, continuous at every x?

A: Given: fx=-2,    x≤-1ax-b,    -1&lt;x&lt;13,   x≥1

Q: For what value of the constant c is the function f continuous on (-o, o)? { Cx2 2x if x < 5 - x3…

A: Observe that, f (x) has discontinuity at x = 5.If it is continuous at x = 5, then continuous on…

Q: For what value of the constant c is the function f continuous on ( - 0, 00) where cx + 6 if a 7

A: Given      fx = cx+6            if x≤7cx2-6          if x&gt;7To find      Value of c where function…

Q: For what value of the constant c is the function f continuous on (-o0, 00) where S cx + 6 if x E…

A:

Q: For what value of the constant c is the function f continuous on (-o, co)? ( cx2 + 8x if x < 3 f(x)…

A: Given: For what value of the constant c is the function f continuous on (-infinity, infinity)

Q: Зx2 — 1 Q7- Let f(x){ cx + d Vx + 8 if x 1 Determine e and d so that f is continuous everywhere (as…

A:

Q: For what value of the constant c is the function f continuous on (-0, 0) if x < 5 f(x) ={ cx? + 8x…

A:

Q: The value of k that makes x2 – kx + 2x – 2k f(x) x # -2 x + 2 4, continuous at x = -2 is x = -2 O 2…

A:

Q: If F(x) is an antiderivative of x2 + x1, then what is the value of F(1) - F(-1)? O -2 O -1

A:

Q: For what value of the constant c the function f continuous on (-o, co)? S cx? + + 9x if x < 4 f(x) =…

A:

Q: 4 Suppose that f(1) = 9, f(4) = -7, f'(1) = 6, f'(4) = -1, and f" is continuous. Find the value of…

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Q: (a) If e19z f (2) = z10 + 49 at how many points the function f (z)is discontinuous ?

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: 2. Supposethat f(x)=?βx? −3 if βx + 2 ifx≤2 x &gt; 2Find the value of β so that f(x) is continuous…

A:

Q: -Q3/As the function f(x,y) = at (-1,2) xy 1 + x² + y² is Continuous

A: Here we have to check the continuity of the function at the given point.

Q: cx +5 f(x) = for x 2

A: Explanation of the answer is as follows

Q: Find the particular antiderivative F(x) of f(x)=4x−3 that satisfies F(1)=8.

A: The given function f(x)=4x-3, its antiderivative satisfies F(1)=8

Q: For what value of the constant c is the function f continuous on (- o, 0) wh- cx + 7 if x 8 C =

A:

Q: 45. For what value of the constant c is the function f continuous on (-∞, ∞)? Scx? + 2x if x 2

A: Let f(x)=cx2+2xif x&lt;2x3-cxif x≥2

Q: 3. For what value of a, f(x) is continuous at every x? Sx2 – 1 2ax x 3 f(x) =

A:

Q: For what values of a and b is ах + 2b, x² + 3a – b, Зх — 5, 0 2 |continuous at every x?

A: Given:

Q: The function f(x) =x + 1/x is concave upward on none O (-1) O (0,) O (0,1) O (1,)

A:

Q: For what values of a and b is

A:

Q: If F(x) is an antiderivative of x2 + x*1, then what is the value of F(1) - F(-1)? O -1 O 3 O -2

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Q: If f(1) = -0.6, f'(x) is continuous, and f'(x)dx = -12.2, what is the value of f(4)? %3D

A:

Q: Suppose that f(x) = SBx? – 3 if if (Bx+2 x> 2 Find the value of B so that f(x) is continuous…

A:

Q: (3) If | f(x) dx exists and c is a real constant, prove that | f(2) dar = |_ f(r + c) dr.

A: We use definite integral properties to prove this statement

Q: If F(x)=∫e^(5t2) dt over interval [3x, 4x^2], what is F′(x)? (Do not include "F′(x)=" in your…

A: Given,  over the interval  .

Q: 2 If f is continuous on [0, 2] and f(x) dx = 5, find the value of | f(æ – 2) dæ.

A:

Q: 9 3 Iff is continuous and f(x) dx 8, find f(x2)dx

A: Given as

Q: For what value of the constant c is the function f continuous on the interval (-oo, oo). Sz² - 9, 8z…

A:

Q: For what value of the constant c is the function f continuous on the interval (-o, 0). f(x) = { x² -…

A: we have to find c

Q: For what values of a and b is ax + 2b, g(x) = {x? + 3a - b, 0<xS2 3x 5, %3D - continuous at every x?

A: The given function is gx=ax+2b,        x≤0x2+3a-b,  0&lt;x≤23x-5,           x&gt;2. For the given…

Q: (2) Is the function f(x) : R → R, sin a 1 ifa # πh,k & Z, ifa = Tk, k ε Z f (x) Borel measurable?

A: Consider the given function, fx=1sinxifx≠πk,k∈Z1ifx=πk,k∈Z   Thus, the given function have infinite…

Q: | For what value of a is Sx² – 1, x< 3 |2ax, f(x) = continuous at every x?

A: Let f is continuous at x = 3 then left and right limit are equal.

Q: If the function f (x) = } 6x – 4, x5 is continuous at x =5, then the value of k is %3D %3D O a. 10 O…

A:

Q: If f(2) = 14, f' is continuous, and f'(t)dt = 23, what is the value of f(5)=? %3D

A: Given :

Q: Find the values of a and b that make f continuous everywhere. x2 - 4 if x < 2 X - 2 f(x) if 2 s x <…

A:

Q: Find the values of a and b that make f continuous everywhere. x2 - 4 if x < 2 x - 2 ax? - bx + 3…

A:

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.