Need help with calc 201

[mlane]

I am having a little trouble with instantaneous velocities. It made perfect sense in class. Also, I am a little rusty on algebra skills also. one of my problems is:lim as h goes to 0. [((4+h)^1/2)-2]/h. I know I have to multiply by ((4+h)^1/2)+2 in the denominator and numerator but I get stuck and am missing a step in getting the radical out of the denominator. the answer is suppose to be 1/4. can u help

 

[wjm11]

I am having a little trouble with instantaneous velocities. It made perfect sense in class. Also, I am a little rusty on algebra skills also. one of my problems is:lim as h goes to 0. [((4+h)^1/2)-2]/h. I know I have to multiply by ((4+h)^1/2)+2 in the denominator and numerator but I get stuck and am missing a step in getting the radical out of the denominator. the answer is suppose to be 1/4.

Hi, mlane,

You’re doing fine. You don’t have to get the radical out of the denominator; after simplifying, you’ll end up with

lim as h goes to 0 of 1/((4 + h)^.5 + 2) = 1/((4 + 0)^.5 + 2) = 1/(2+2) = ¼

Hope that helps.

 

[mlane]

radical in proble,

Thanks for the reply. am i suppose to assume that h is extremely close to zero and replace it with zero to solve this? I was trying to get it to cancel somehow.

 

[tkhunny]

Substitution is not appropriate, though many use it to solve limit problems. The premise of this limit is that h APPROACHES zero (0). This necessarily means that h ≠ 0. Clearly, the simple substitution is missing the point. Your task is to determine what the limit is. Sometimes it requires imagination.

Some are easy:

What is the limit of 1/x as x approaches zero?
What is the limit of x as x approaches zero?

Some are pretty tricky until you have more tools.

What is the limit of sin(x)/x as x approaches zero?
What is the limit of x^x as x approaches zero?

Some are just plain irritating because they LOOK easy, but they are not.

What is the limit of (1+x)^1/x as x approaches zero?