Question: If and exist but are not equal, then is not differentiable at c, and the graph of has a corner at c. Prove

If lim h0- f(c+h)-f(c) hand lim f(c+h)-f(c) h0+ h exist but are not equal, then ƒ is not differentiable at c, and the graph of ƒ has a corner at c. Prove that f is continuous at c.

lim h0- f(c+h)-f(c) h

Step by Step Solution

★★★★★

3.40 Rating (156 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

that The function f is continuous at x c if lim fx fc or equivalently if limf... 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:

Managing Scope Changes Case Study Scope changes on a project can occur regardless of how well the project is planned or executed. Scope changes can be the result of something that was omitted during...

Q:

On-the-job training (OJT) has three drawbacks. Briefly discuss these and the possible solutions suggested by experts in the field.

Q:

The preceding exercise may fail if the terms are not positive. For example, let aij := +1 if i - j = 1, aij := -1 if i - j = -1, and aij := 0 elsewhere. Show that the iterated sums Both exist but are...

Q:

Answer the following True or False: If f (a) is continuous at x - 9 and f (9) = -8 then lim f (x) = -8. O True O False Submit Question7z -6 if x -2 O Continuous at x = -2 Not continuous: f (-2) does...

Q:

Answer the following True or False: If f (a) is continuous at x - 9 and f (9) = -8 then lim f (x) = -8. O True O False Submit Question7z -6 if x -2 O Continuous at x = -2 Not continuous: f (-2) does...

Q:

Many diabetics need to control their blood sugar levels with insulin. A graph is given that shows blood sugar levels over time after insulin is given to a non-diabetic person at time, t = 15 minutes....

Q:

1. (60 pts True/False. Indicate whether the statement is true or false. If the statement is false, present an explanation or counterexample. (No explanation necessary for each true statement.) (2...

Q:

seventh pages Chapter 3 Curve Sketching How much metal would be required to make a 400-mL soup can? What is the least amount of cardboard needed to build a box that holds 3000 cm3 of cereal? The...

Q:

1. True / False. Every function f that is differentiable on the closed interval [ a , b ] is itself the derivative of some function g on the same closed interval [ a , b ] . Explain your reasoning if...

Q:

please this calculus homework in detail and ensure no ai generated work. This is for grade 12 calculus & vectors. Thanks for your help :) Reminder: Taylor Series expansions and special rules from...

Q:

Using EES (or other) software, determine the effect of the amount of air on the adiabatic flame temperature of liquid octane (C8H18). Assume both the air and the octane is initially at 25C. Determine...

Q:

How practical would it have been for Paulson to tell customers that it had not approved of these particular securities?

Q:

When its assumptions are satisfied and a stock is selling for its intrinsic value, the constant - growth dividend discount formula can be inverted to infer the rate for the stock.

Q:

Whether people would be much better off without society regimenting their lives and even their deaths. (Indicates antiauthoritarian attitudes.) AppendixLO1

Q:

The velocity function (in meters per second) is given for a particle moving along a line. Find (a) The displacement (b) The distance traveled by the particle during the given time interval. v(t) = 3t...

Q:

The acceleration function (in m/s2) and the initial velocity are given for a particle moving along a line. Find (a) The velocity at time t. (b) The distance traveled during the given time interval....

Q:

The linear density of a rod of length 4 m is given by ((x) = 9 + 2x measured in kilograms per meter, where x is measured in meters from one end of the rod. Find the total mass of the rod.

Q:

23. What must be the price of a $1,000 bond with a 6.4% coupon rate, annual coupons, and 15 years to maturity if YTM is 10% APR? O A. $726.18 O B. $871.42 O C. $580.94 OD. $1,016.65

Q:

Suppose that on October 24, 2015, a company sells one April 2016 live-cattle futures contracts. It closes out its position on January 21, 2016. The futures price (per pound) is 121.20 cents when it...

Q:

factors causing opioid increased visits to ER ? WHAT CAN WE DO ABOUT IT ?