All the following functions have continuous extension at x = 0 EXCEPT. Select one: a. None of them b. f(x) = x?cos O C. g(x) = x²tan--) d. h(x) = sgn(x) e. k(x)= =x² x + X 2.

Q: 4. h(x) = x-T at X %3D 2. 5h(X) = x + x4-1 at X = %3D

A: Continuous function at x=a

Q: Is the function continuous on the interval (0, T COS x O no O yes O cannot be determined

A: Given problem:- Is the function ex/cosx continuous on the interval [0, π] ?

Q: If fx) is a continuous function on [4,7] and F(x) is an anti-derivative of f(x) such that F(4)=9 and…

A: Given f(x) is continuous on [4, 7] and F(x) is the anti-derivative of f(x)                 F (4) = 9…

Q: Consider the following example: if g: [a, b] → R is continuous and F is a function defined as F(x) =…

A: It is given that,  g : a, b → ℝ is continuous and F is a function defined as ;  F(x) = 1,x∈a,…

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

A: Consider the given piecewise function

Q: If f(x) is continuous in the interval [-2, 1], ƒ(−2) = −4, and f(1) = -1, can we use the…

A:

Q: x< x3 B- If f(x) = Ax? is continuous at x = ; Find A? HIN IN

A: We are given : f(x)=x3       , x&lt;12Ax2     ,x≥12 is continuous at x=12 Condition for f(x) to be…

Q: sinkx) x 0

A:

Q: Suppose h' is continuous x>0. IF x = 0 and h'(x) = 3√tan (2x)-1 it exists. i at Find h (0), 'F

A: For the solution of the problem follow the next step.

Q: VI. Suppose h' is continuous at x = 0 and h'(x) =tan(2x) - 1 if x > 0. Find h(0), if it exists.

A: Let's find.

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: A. Consider the function defined by [x² +1, if x<5 f (x)={ |6x– 4, if x25 a. Is f continuous at x =…

A:

Q: Suppose f is a continuous function such that Si f(t)dt = e® In(x) for all x > 0. What is the value…

A:

Q: Consider the following example: if g: [a, b] → R is continuous and F is a function defined as F(x) =…

A: Please comment if you need any clarification. If you find my answer is useful please put thumbs up.…

Q: Suppose that  ff"' is continuous and f'(c)  =f"(c) =0 , but f"'(c) &gt;0. Does f have a local…

A:

Q: define the function at 5 so that it becomes continuous at 5.

A: First, we rationalize the function, so that it becomes continuous at 5 which is shown on the board

Q: 7. If f is a continuous function such that f(t)dt = x sin x + f(t) dt for all x , find an explicit…

A:

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…

A:

Q: Consider the following. PX)={ S-5x, f(x)= x² – 2x + 5, X 4 Find the x-value at which f is not…

A: Consider the given function   Here the objective is to find the value of x at which f(x) is not…

Q: Assume that ƒ is continuous on [0,1] and that f(0) = 2 and f(1) = 1. Show that the graph of y = f(x)…

A: given  f is continuous on [0,1] f0=2,f1=1y=x2+1

Q: 17.Determine the following function if continuous at p(x) = 3x? – x +5 ;at x = 1 A. discontinuous at…

A:

Q: Q2. Let f:R→ R be a function such that f(x) = x sin (-) has a limit at xo + 0. If f is defined at xo…

A:

Q: Prove that the following continuous function has at least one real root; h(x) = −2x + 3 − ln x

A:

Q: (d) A function not continuous at 0 such that (f(x))4 is continuous at 0.

A:

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: Show that the function below is continuous at x 0 (cos x-1 f(x) D if x<0 5x, if x20

A:

Q: Let f be defined by the following. S2x-3 f(x) = 6 - x if x < 3 if x 2 3 (a) Is f continuous at x =…

A:

Q: Is the following piecewise defined function f(x) continuous at x = = 0, [cos(x), x≤0 f(x) = x²+x+1,…

A: The given function is: fx=cos x,       x≤0x2+x+1,  x&gt;0 Check whether the function is continuous…

Q: 1. Where are the following functions continuous? x F(x) = ex + 4-x3 G(x) = 3x5 - 4x? H(x) = x-5x3…

A:

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: b) Show that the function sin for æ e (0, 1] { f (x) = for æ = 0 is absolutely continuous on [0, 1].

A: Function is called continuous function if the left and right hand limit values at each and every…

Q: Determine if the function f below is continuous at x = 1: ſ1– VT- x, x 1

A: According to question,given function,fx = 1-1-xx≤1ln xx&gt;1

Q: 2. Consider the function f with domain (-2, 0): 3|22 – 1| if – 2<r<1 2.r2 + 2x – 4 f(x) = 3 if r = 1…

A:

Q: x²-1 for x# 1 - If flx) = show that flxx) is continuous at x = 1 x-1 2 for x = 1,

A: topic - limits and continuity

Q: 13. Let g be defined by V7x +2 V6x + 4 | g(x) = if x 2 - and x 2 x – 2 k , if x = 2 For what value…

A: The given functiong(x)=7x+2-6x+4x-2,if x≥-27 and x≠2k,if x=2

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

A:

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=?

A:

Q: If f(x) is a continuous function such that it is increasing on [1, 3], then Si f(x)dæ is less than…

A:

Q: Is the following statement correct? If the function f is continuous at x=1, then the constant a…

A:

Q: . Is f(x)= Vx + 1 continuous at x == -1? Yes, because all functions are continuous No, because the…

A:

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

A:

Q: Find a constant b such that h is continuous at x = 2, where x +1 for |x| 2 With this choice of b,…

A: It is given that the continuous function  hx=x+1for x&lt;2b-x2for x≥2 It is also given that function…

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

A:

Q: h(x) = x+1 %3D at x = 1 x2-1

A: Function f(x) is continuous at a point x=a :Function should be defined at x=a, and  limx→a-f(x) =…

Q: 2. h(x) = at x = 1 x+1 %3D x2-1

A:

Q: 3. Consider the function f(x) : (0, 00) → R where f(x) = . (1) Show by definition that f is…

A:

Q: Which of the following functions will not be continuous at x = -5? Select one: a. All of these…

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.