Sunday

February 1, 2015

February 1, 2015

Posted by **Anonymous** on Sunday, September 19, 2010 at 12:00pm.

x^2+a if x<0,

2x+a^2 if 0 less than or equal to x less than or equal to 1,

3 if x>1

a. determine the value(s) of a that will make f(x) continuous at x=0

b. determine the value or values of a that will make f(x) continuous at x=1

- calc -
**bobpursley**, Sunday, September 19, 2010 at 12:01pmI will be happy to critique your thinking.

- calc -
**Anonymous**, Sunday, September 19, 2010 at 12:11pmFor part a I took the limit as x tends to zero from the right of 2x+a^2. I put zero in for x and then said a=0 which would also make the limit as x approaches zero from the left of x^2+a 0 so the function would be continuous.

I don't know how to start part b because there is no variable for x>1

- calc -
**bobpursley**, Sunday, September 19, 2010 at 12:13pmYou are correct, part of 3 is missing.

- calc -
**Anonymous**, Sunday, September 19, 2010 at 12:14pmMaybe the limit of x approaches 1 from the right of 3 = 3. And then set the limit of x approaches 1 from the left of 2x+a^2 = 3 and then solve for a and get 1.

- calc -
**bobpursley**, Sunday, September 19, 2010 at 12:15pmI am not certain I would make that assumption on the problem. However, you could be right.

- calc -
**Anonymous**, Sunday, September 19, 2010 at 12:17pmone more question.

if possible determine the value(s) of a that will make f(x) continuous on (negative infinity, infinity)

- calc -
**MathMate**, Sunday, September 19, 2010 at 1:02pmThere is more than one value of a that will make the function continuous at x=0, since at x=0,

x^2+a =2x+a^2

or setting x=0,

a-a²=0

a(1-a)=0

giving

a=0 or a=1.

Now you can continue with the last part.

**Answer this Question**

**Related Questions**

calculus - Consider the function f(x)=65x−cos(x)+2 on the interval 0 less ...

Calculus - Consider the function f(x)=6x-cos(x)+5 on the interval 0 is less than...

i lied. very quick calc problem. - f(x) = abs(sin(x)), -pi less than or equal to...

Algebra 2 - Okay so I need help with basically how to find the domain, range, ...

math - The function f(x)is defined as f(x)={-2x+3: if -2 less than or equal to &...

calc ii - if we know that 12 is less than or equal to f(x) which is less than or...

Calculus - Consider the function f(x) = x^4 - 72 x^2 + 3, -5 less than or equal...

Algebra - If 1.2 is (less than or equal to) a (less than or equal to 5.1 and 3 (...

ap stats - Continuous Random Variable, I Let X be a random number between 0 and ...

stats - Continuous Random Variable, I Let X be a random number between 0 and 1 ...