If f(x) is continuous at x=a , then f(x) is also differentiable at x=a.

Q: 'he function f: E → R is uniformly continuous if

A: We have to find the answer using the definition of uniform continuity.

Q: If f is differentiable at a, then f is continuous at a.

A: If a function fx is differentiable at x=a then function must be continuous at x=a. But a function…

Q: If the derivative of y = f(x) at x = 2 is equal to " (0 " then y = f(x) is not continuous at r = 2.…

A:

Q: Is f(x)= Vx + 1 continuous at x == -1

A: Draw the graph and check continuty with help of limit of function.

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

A:

Q: Use the chain rule to show that for any differentiable function f(x), [e/(e) = f(x)e/(=),

A:

Q: (tan ) 1/x TC + x 4 * f(x)D. k, For what value of k, f (x) is x =0 continuous at x = 0?

A: The

Q: If f is differentiable at a number, x, then f is continuous at x.

A:

Q: If f(x) is continuous at x = c then f'(c) exists. True False

A:

Q: B) Show that fx) = sin for x * 0. for x= 0. X = is not continuous.

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: If f(g(x)) is continuous at 0, then g(x) is continuous at 0  true or false

A: Given that If f(g(x)) is continuous at 0, then g(x) is continuous at 0

Q: Suppose that f(1) = 3, f(4) = 5, f '(1) = 4, f '(4) = 4, and f " is continuous. Find the value of xf…

A:

Q: If f is continuous everywhere except at x = 2, then f(x +1) dx is not integrable. True False

A: To check whether the given statement is True or False."If f is continuous everywhere except at x=2,…

Q: If ƒ is differentiable at a, must ƒ be continuous at a?

A: we know that for a given function if it is differentiable at given point then it must be continuous…

Q: If f(x) is differentiable at x = a then f(x) is also continuous at x = a. A True B False

A:

Q: Let f(x) be a continuous differentiable function that f(x)- 4 satisfies lim =D5 %3D x3 x-3 Which…

A:

Q: Find the derivative of f(x) at r = 0 using the definition of the derivative as a limit. %3D Va +I

A:

Q: Let f(x) E R[x]. If f(a) = 0 and f'(a) = 0 [f'(a) is the derivative of f(x) at a], show that (x –…

A: Given: f(a) = 0, f'(a) = 0 [f'(a) is derivative of f(x) at a] To Show: (x-a)2 divides f(x) Concept…

Q: Use limits to determine if f(x) = 1 is continuous at x = 0. (z+2)?

A:

Q: Set f(x) = xª for x ≥ 0 and f(x) = 0 for x < 0. For which values of a is f continuous at 0, and for…

A:

Q: Let f(x) = 3√(x + 1) − 4 = (x + 1)1/3 − 4. Use the limit definition of the derivative to show that f…

A: Consider the given function: fx=x+13-4=x+113-4 Vertical tangent at point indicates that at that…

Q: Find a positive value, c, for x, thot satisfies the Mean valve Theorem for derivatives for…

A:

Q: Prove that if the function f : I → R has a bounded derivative on I, then f is uniformly continuous…

A:

Q: Find the local linear approximation L (x) of the function f(x) = 5 – x² at =2.

A: To find the linear approximation of given function.

Q: Let 'f be a continuously differentiable real valued function defined bx+a x<1 by f(x) = 5x² Then the…

A:

Q: show that f,given by f(x) x +0 )is continuous on R-{0}

A:

Q: Find the linearization L(x) of the function at a. f(x) = sin(x), a =. 3 L(x) =

A:

Q: lim, f(x)= 0, then | f(x)dx diverges

A: Statement:  limx→∞ f(x)≠0,  then ∫1∞ f(x) dx   diverges.

Q: Let f be a continuous function such that f (x) dx 5 and 6° | f(x) dx = 3. What is the value of |…

A:

Q: Let f(x) E R[x]. Suppose that f(a) = 0 but f' (a) + 0, where f' (x) is the derivative of f(x). Show…

A:

Q: continuous at (C

A:

Q: If f is continuous on [0, 1], prove that f₁¹ f(x) dx = f₁¹ ƒ(1 − x)dx.

A: This question can be solved using properties of definite integrals.

Q: Is f(x) = √x continuous at x = 0?

A:

Q: Find the linearization L(x) of the function at a. f(x) = sin(x), a = 3 L(x)

A:

Q: If f is differentiable at a ,then f is continuous at a

A: Every differentiable function is continuous.

Q: Find the linearization L(x) of the function at a. п f(x) = sin(x), a = 6 L(x) =

A:

Q: If f(z) is continuous at z then it must be differenttiable at z, 0.

A:

Q: Prove that the function f(x)=sinπ|x| is continuous at x = 0 but not differntiable at the same point.

A:

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

A:

Q: Show that f(x) := x/3, x e R, is not differentiable at x 0.

A:

Q: 1. Show that the function x2 – y2 2xy f(x,y) ={ x2 + y? if (x,y) # 0 if (x, y) = 0 is continuous at…

A: If for every ε&gt;0, there exists a δ&gt;0, such that if |x-a|&lt;δ, |y-a|&lt;δ, then the function…

Q: The general anti-derivative of the function f (x) - In(x) is given by x In( x)+ C Inx)-x+ C x In(x)…

A: The integral (anti derivative) of fx=lnx can be evaluated by using integration by parts. The…

Q: 34. Show that f(x) = Jã is not differentiable at x = 0.

A:

Q: Prove f (x) 1+ mx is continuous at x = 1, where m e R

A:

Q: d. Use the limit definition of the derivative, f (x) = lim f (x+h)-f(x) 1 +h)=j, to prove that VT =…

A:

Types of Bias

Statistics is the study of data collection, organization, analysis, interpretation, and presentation. Statistical bias is a characteristic of a statistical technique or its findings in which the expected value deviates from the actual root quantitative parameter being estimated. According to the actual definition of bias, it refers to the tendency of a statistic to overestimate or underestimate a parameter.