2. Determine whether f is continuous or discontinuous at 1. (x – 1 if x > 1 f(x) -x² if x <1 O f is continuous at 1. O f is discontinuous at 1.

Q: (5) Use the limit definition of derivative to prove the following: (a) For any a e R, (f(ax))' =…

A:

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: b) Suppose that f(x) 1 if x is negative. Can ƒ be continuous at x = 0?

A:

Q: 2. ASSUME f(x) IS CONTINUOUS AND DIFFERENTIABLE ON AN OPEN INTERVAL AS GRAPHED. WHICH OF THESE…

A: Since you have posted multiple question in this question so I have solved first question as per our…

Q: Where is f(x) = x-5 x² –6x+5 discontinuous? f (x)is continuous everywhere o 5 o 1 о 5, 1

A:

Q: Suppose f' (x) = g (x) (x + 1) (x – 2)´, where g (s) is a continuous function which is always…

A: When f'(x)&gt;0 then function increasing when f'(x)&lt;0 then function decreasing

Q: 3. Define the function sin(2x – 2) x 3 3' - Determine if f is continuous at x = 1 and x = 3. If…

A:

Q: 8. Suppose that f is a continuous function such that f'(x) > 0 for all æ, f(0) = 0, and f(1) = 1. If…

A: f'(x)&gt;0 for all x, f(0)=0 and f(1)=1.To Find: If ∫01f(x)dx=13, find the value of ∫01f-1(x)dx.

Q: 10. Consider the following function. 1 x } x > Find the values of a and b that make f(x)…

A:

Q: Show that g(x) = (x3-8) / (x-2) has a removable discontinuity at x = 2. How should g(2) be defined…

A: The left-hand limit of a function at a point is the value of the function at a point very close from…

Q: Determine if the following functions are continuous at the given value of x. 1. f(x) = 3x? + 2x + 1…

A: continuty

Q: Find c so that f is continuous at every point f(x) = 5x+12c, if x < -5 f(x) = (cx^2)+1, if x ≥ -5

A: Given- fx=5x+12c if x&lt;-5cx2+1   if x≥-5 To find- The value of c that  the above function is…

Q: 18. Suppose that f is a differentiable function such that f(g(x)) = x, and f'(x) = 1 1+(f(x))². Show…

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: For all but two choices of a, the function (x) = x if xS a and x' ifx > a will be discontinuous at…

A:

Q: Define f:R → R by f (x) = 5x if x is rational and f (x) = x² + 6 if x is irrational. Prove that f is…

A: Given, f:R→R by f(x)=5x if f(x) is rational and f(x)=x2+6 if x is irrational.To prove that f is…

Q: Which of the following statements is not true, 3x² + 4x – 4 if x 1 f is discontinuous at æ = f is…

A: Given, f(x)=3x2+4x-44x2+7x-2,if x≤-1x2+3x+3,if-1&lt; x&lt;14x+5if x≥1 now put x=-2 in funcion…

Q: If a function f(x) is not defined at x-c, then it is not continuous at a close interval [a, c). * O…

A: We know that function is continuous at c if the 1) f(c) is defined 2)limit of f(x) exist, Here…

Q: Suppose a function f is continuous on [0, 1], except at a = 0.25, and that f(0) = 1 and f(1) = 3. Is…

A:

Q: Suppose X is continuous with f(x) = x/2 from 0 to 2. What are the values of f(1) and P(X=1)? 1/2 and…

A: Given,f(x)=x2 ; 0&lt;x&lt;2

Q: (b) Redefine f(4) so that f is continuous at x = 4 (and thus the discontinuity is "removed"). f(4) =

A: The given function is: f(x)=x2-12x+32x-4

Q: 3) See the attached file 3-Let F(x)= {* - 1 Vx -1 is the function continuos „x > 2 at x=2 OA)…

A:

Q: 1. Find the x-values (if any) at which f is not continuous. Which of the discontinuities are…

A:

Q: Consider a continuous function f(x)=2ex−1−2x. The graph of f is decreasing on which interval/s?

A:

Q: Which of the following graph shows that f (z) = |r - 2| is continuous but not differentiable at x =…

A:

Q: 19.D. Show that the function defined by g(x) g² sin (1/x), x * 0, %3D = 0, 0, is differentiable for…

A:

Q: 3. Find the value of k that will make f continuous on (-o, 00). NORS x + 19 if x 1

A:

Q: Evaluate f (x): at x = -2. %D 1 - x2 Select one: A. Discontinuous B. Continuous

A:

Q: For all but two choices of a, the function (x) x if x a will be discontinuous at the point x = a.…

A:

Q: , for x 1 Let f(x) be a function de fined by f(x)3= Discuss the contuniuty of f andf".

A:

Q: 3. Consider the function g(x) defined by | 22 sin(1/x) if x > 0, g(x) = –x² if x < 0. (a) Show that…

A:

Q: Consider the following f(x)= 2/4-x2 Find the x-values at which f is not continuous. Which of the…

A:

Q: 2. For the given function, f, determine if the function is discontinuous at a given point. State…

A: Function is f(x)=xx a=0 We have to check whether the function is continuous or discontinuous at…

Q: Find number k, so that f is continuous at every point. tan kx f(x) = x 4x+3 k2, x 20 O O and= Cannot…

A: The function is given by fx = tankxx ,x&lt;04x+3k2 ,x≥0 To evaluate : The value of k so that f is…

Q: Consider f(x) = #3/5. Is f(x) differentiable at x=0? Is f(x) continuous at x=0?

A: The given function is,

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

A:

Q: 10.C. If f is defined and continuous on R to R and if f(xo) > 0, then is f positive on some…

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: - 35) Prove that if y=flx)is continuoUS and flx1= 0 when x is a rational number, then f Lx)=0 for…

A: The objective is to show f(x) =0 for all x belongs to R.

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: 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: . Is the function continuous on the interval (4, 10)? (x + 1 if x > 8 f(x) = E) + 7 if x < 8 A.…

A:

Q: 4. Use the limit definition of the derivative to test whether the following function f(x), given by…

A:

Q: 4. Discuss the continuity of the function f at x = 0. Iff is discontinuous at x = 0, is it…

A:

Q: If a function f is continuous at 0, show that g(x) = xf(x) is differentiable at 0 and find the value…

A:

Q: B. so, find f'(2). If not, explain why not. It can be shown that f is continuous at x = 2. Isf…

A:

Q: Consider the piecewise-defined function Ax if x 0 h(x) е (a) Give values for A and B so that h(x)…

A: Given Data: Function: hx=Axif x≤0e-1/x+Bif x&gt;0 (a) The condition for the continuous function is,…

Q: 3. Consider the function g(x) defined by { x² sin(1/x) if x > 0, g(x) = if x <0. (a) Show that g(x)…

A:

Q: 2. Consider the function f(x) = if x = {9 in lowest terms q > 0, p,q e Q; 0 if x e Q°,x = 0…

A: We use sequential approach of continuity to show it.

Q: ⎪ ⎨ ⎪ ⎧x^2 − 1 , − 1 ≤ x < 0 2x , 0 < x < 1 1 , x = 1 −2x + 4 , 1 < x < 2 0 , 2 < x < 3 a) Is f…

A: