Determine the values of A for which h(x) is continuous. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) if x < 3 5x h(x) = if x = 3 x² – 17 if x > 3

Q: e that f(x) is continuous, and f'(x) is given in the figure below. y y = f'(x) 1 3

A: In this question we will use basic of calculus i.e concept of maximum and minimum. Solution of the…

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A: The given function is continuous for all x&lt;0 and for all x&gt;0, because it is a polynomial…

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: If f and & are continuous function of *, which of the following is true? F (x) dx+ (x) dx -dx: 8(x)…

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Q: For what values of b is b + 1' x? + b, x > 0 8(x) = continuous at every x?

A: Now we check the continuity at x = 0:

Q: If f is a piecewise continuous and T-periodic, then show that for a e R T ra+T f (x) dx = - (2) f…

A: i used the change of variable formula to obtain solution

Q: Find the values of α and β such that the function f(x) = ( α cos x + 2 if x < 0 βe3x + αx2 if x ≥ 0…

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Q: Find a constant c such that x² – c2 if x 4 g(x) ={ is continuous everywhere.

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Q: For what value of b is X - b b + l' x 0 continuous at every x?

A: The given function is gx=x-bb+1if x&lt;0x2+b if x&gt;0. If the above function is continuous at x=0,…

Q: For what values of b is - b b + 1' g(x) x? + b, x > 0 continuous at every x?

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Q: sinkx) x 0

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Q: Find a value of x, if any, at which f(x) = x + 2 - is not continuous. x2 + 4 If f(x) is continuous…

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Q: For what value of b is

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Q: 2. If f is a continuous function such that S(t)dt = cos(2x)e* - [e s(t)dt for all x, find an…

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Q: Find a value of x, if any, at which/(x)= Vx- 27 is not continuous.

A: We will check the continuity of the function

Q: Iff is continuous at a point a and c e R, then cf is continuous at a.

A: Note that, f is said to be continuous at 'a' if limx→af(x)=f(a) And, (cf)(x)=cf(x)

Q: 4 – x² p(x) = x – 1 at x = 0 Select the correct response: Continuous O Discontinuous

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Q: Find the value(s) of k that makes the function continuous over the given interval. a < k k < a S 3x…

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Q: find constants a and b such that f(2) +3 = f(0) and f is continuouspiecewise f(x) = ax + b , if…

A: We have been given a piecewise function and a condition f(2)+3=f(0) and the fact that f(x) is…

Q: Find a value of x, if any, at which f (x) = Vx – 64 is not continuous. ff(x)is continuous for all…

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Q: Given a continuous function of which is twice differentiable, if f" (c) > 0, which of the following…

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

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Q: For f(x) = Vx ln x, find a). domain and f', b). the intervals on which f is increasing or…

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Q: Find numbers a and b, and c, so that f is continuous and differentiable at every point. 4) x- + C,,…

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Q: ) For what value of a is fx² -1 x<3 S(x)= { |2ax x23 Continuous at every x?

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Q: If f(x) is a strictly increasing continuous function with domain [0, 00]. If f3(x) = tf()dt. 0, Find…

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Q: d lim g(q)d q→7 (dg

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Q: 4. For a function f:D → R and a point xo in D, define A = {x in D x ≥ xo} and B: {x in D x ≤ xo).…

A: Recall definition of conituity as, Right hand limit = left hand limit = value of function at the…

Q: Consider the function xe* if x < 0 g(x) = x³ – 2x2 + x if 0 < x < c , %3D if x 2 c where c is a…

A: Given,gx = xex                            if x≤0x3 - 2x2 + x          if 0&lt;x&lt;c1x…

Q: Find the values of c that make f continuous everywhere: x? – c2 if x 8 smaller c = larger c = Use…

A: Given function fx=x2-c2if x&lt;8cx+6if x≥8 The given function is continuous at x=8 then,…

Q: - f(æ) = Where is %3D discontinuous? x2 + 3x – 18 - o f(x) is continuous everwhere O 3 O-3 and 6 O-6…

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Q: Consider g(x) = rº/3. Is g(x) differentiable at x=0? Is g(x) continuous at x=0?

A: We find g'(x) using the power rule  Then we find the left and right-hand limits of g'(x) and g'(0)…

Q: a. Find the value of (k) that make the fumction flk) = ,continuous atx = 0 +3k-3 x=0

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Q: 4) Find the value of the constant k so that the function (1 – k, if z<3, f(z) = 1– kr, if 123, is…

A: This question is related to limit and continuity of a function, we will use condition for a function…

Q: Find a value of x, if any, at which f(x) = Vx – 8 is not continuous. If f(x) is continuous for all…

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Q: Find c such that the function 10 I C - is continuous everywhere.

A: A function f(x) is said to be continuous at a point x=a if limx→af(x)=f(a). That is, a function f(x)…

Q: Find the values of a and b such that the following function a² cos(x − 2) — 26(³-x), if x 2, is…

A: Topic = Limits

Q: f is continuous and f(x) dx = 8, find xfc

A: we have to find

Q: The table shows selected values for a continuous functiong that is increasing over the interval [0,…

A: Consider an interval a,b and its partition a=x0&lt;x1&lt;x2&lt;⋯ &lt;xn=b. Then the integral ∫abf(x)…

Q: j(x) = v2x – 4 %3D

A: We have  jx=2x-4   Function is continuous when 2x-4≥02x≥4x≥2

Q: . For what value(s) of c is f(x) = 54-x³, x < 3) %3D lcx² + 13, x 2 3) continuous everywhere?

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Q: 6. gx) VX- 3 at x = 4 三 7 g(x) at X = 8 三 e1 gCX)= n4ーメ at x =0

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Q: Find the value of c so that f(x) is continuous at x = 3? x2 f(x) = x 3

A: Given query is to find the value of c.

Q: B/ For what value of a is fa continuous at every x? x2-1, x<3 fo 2ах, x2 3

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Q: If ƒ(x) is continuous [-00,b]then on ſf(x)dx= lim [ ƒ (x)dx а. a a

A: Explanation of the solution is given below...

Q: Suppose that h is continuous and h (x) dx = 12. Solve for 2 4 h(v20–4x -dx. Hint: note that h (x) dx…

A: Given that ∫24hx dx=12. Put u=20-4x. Then, du=1220-4x12-1-4 dx On simplifying, du=-220-4x dx

Q: Find a constant b such that h is continuous at x = 2, where h(x) = {x + 1 for lxl &lt; 2 b - x 2 for…

A: Given, hx=x+1x&lt;22b-x2x&gt;2

Q: Find c such that the function x c is continuous everywhere. x² – 8 f(x) = {

A: ANSWER : c = 5

Q: d) Will h(t) be continuous or discontimuous at t = 3 if we use A = 1? If discontinuous, what type of…

A: Here we use the definition of continuity of a function at a point. Which is defined by Left hand…

Q: Q3) For what values of a and b are -x² + a , x Continuous at every x ?

A: