Question: Use the definition of differentiability to prove that if is differentiable at (a, b), then is continuous at (a, b).

Use the definition of differentiability to prove that if is differentiable at (a, b), then ƒ is continuous at (a, b).

Step by Step Solution

★★★★★

3.31 Rating (154 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

Suppose that f is differentiable at a b then we know ... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Calculus 4th Questions!

Q:

Grano BV and Henco BV manufacture fairly similar remote-controlled toy cars. Sido BV, a retailer of children's toys, expects to buy and sell 4000 of these cars each year. Both Grano and Henco can...

Q:

Prove that if f: Rn Rm is differentiable at a Rn, then it is continuous at a.

Q:

Use Exercise 10.7.6 to prove that if f is continuous and periodic on [0. 2Ï] and for k = 0,1,..., then f(x) = 0 for all x [a, b]. 2T f (x) cos(kx) dx = f(x) sin(kx) dx = 0

Q:

Suppose that f: Rn R is differentiable at a and that f(a) 0. a) Show that for ||h|| sufficiently small, f(a + h) 0. b) Prove that Df(a)(h)/||h|| is bounded for all h Rn{0}. c) If T := -Df(a)/f2(a),...

Q:

1.17. Let f : R2 -> R be the function: f (x, y) = Vat+ yt. (a) Find formulas for the partial derivatives or a of and ay 1 of at all points (x, y) other than the origin. (b) Find the values of the...

Q:

please answer these 2.06 Question 9 (3 points) Question 1 (3 points) Use the following graph of f(x) to describe the behavior of f '(x). State where f '(x) is For f(x) =(x -1)' , use the definition...

Q:

For f ( x ) = x 2 f' (x) = lim(x+h)-f(x) (x-1) , use the definition of differentiability h-0 h to determine if f(x) is differentiable at x = 1. A Question 2 (3 points) For f(x) = x , use the...

Q:

For f ( x ) = x 2 f' (x) = lim(x+h)-f(x) (x-1) , use the definition of differentiability h-0 h to determine if f(x) is differentiable at x = 1. A Question 2 (3 points) For f(x) = x , use the...

Q:

$$explain clearly... 2.4 Tangent Lines and Implicit Differentiation 1. At what point on the curve y = sinh r does the tangent line have a slope of 1? 2. Find the point(s) on the graph y = a where the...

Q:

2.06 Unit lest: Derivatives - Part 2 Pool 1 Question 1 (3 points) For f(x ) : (X-1' -, use the definition of differentiability f' (x) = lim f(xth)-f(x) h- 0 h - to determine if f(x) is differentiable...

Q:

2. For what values of a and b is the following equation true? kin(4x) b lim tat = 0. 3. Let f( ) = if I =0 1 if I = 0 (a) Show that f is continuous at 0. (Hint: Use the definition of continuity at a...

Q:

The following data were gathered to use in reconciling the bank account of East Meets West Company: Balance per bank $19,340 Balance per company records 6,480 Bank service charges 50 Deposit in...

Q:

i) Purchase machinery with listed price of Rs. 150,000 and in consideration issued own 14,800 ordinary shares of Rs. 10 each. ii) Purchased a plot of land and issued 15,000 ordinary shares of Rs. 10...

Q:

Problem 1 5 - 8 Valuing Callable Bonds Assets, Incorporated, plans to issue $ 8 million of bonds with a coupon rate of 8 . 2 percent, a par value of $ 1 , 0 0 0 , semlannual coupons, and 2 5 years to...

Q:

A company is considering whether to purchase some machinery that will cost 100 000 but that is expected to give rise to additional cash inflows of 50 000 per annum for four years. The cost of capital...

Q:

Find the coefficient of x 2 in the expansion of (2x + 1) 7 .

Q:

Find the coefficient of x 6 in the expansion of (2x + 1) 8 .

Q:

A brick staircase has a total of 25 steps. The bottom step requires 80 bricks. Each successive step requires three less bricks than the prior step. (a) How many bricks are required for the top step?...

Q:

Efficient market hypothesis breaks down into weak, semi-strong and strong forms. What is closest to to the reality? Why?

Q:

a. Calculate the required rate of return for an asset that has a beta of 1.80, given a risk-free rate of 5.0% and a market return of 10.0%. b. If investors have become more risk-averse due to recent...

Q:

which IP addresses are valid