Math for Econ I- Practice Problems New York University - Math for Econ I Practice Problems New York University 3 Limits and Continuity 1 Compute the

Math for Econ I- Practice Problems New York University -...

This preview shows page 1 - 3 out of 3 pages.

Math for Econ I- Practice Problems New York University 3. Limits and Continuity1. Compute the following limits:x2-4xx2-3x-4=45(b) limh0(4 +h)2-1614+1x116 2. Iff(x) =x2+ 2x, compute the following limits:f(x)-f(1)x-1 3. Find all values ofksuch that the limit exists. Then, in each case, find the limit.(a) limx4x2-k2x-4 4. Findkso that the function is continuous everywhere.f(x) =(kx0x <23x22x Thusk= 6.
5. Is the following function continuous on [-1,1]?f(x) =x|x|x6= 0x= 0 Solution Forx >0, we have|x|=x, sof(x) = 1. Forx <0, we have|x|=-x, sof(x) =-1. Thus, the functionis given byf(x) =1x >x= 0-1x <1,sofis not continuous on any interval containingx= 0. 6. Use the definition of continuity and the properties of limits to show thatf(x) =x2+7-xis continuous ata= 4. Solution: 7. For what value of the constantcis the functionfcontinuous on (-∞,)?f(x) =(cx2+ 2xifx <2x3-cxifx2 Solution: 8. Find the numbers at which the functionf(x) =x+ 2 ifx <2x2if 0x12-xifx >1is discontinuous. Solution:
9. Show that the equationx4+x-3 = 0 has a root in (1,2). Solution: 10. Show that the absolute value functionf(x) =|x|is continuous everywhere. Solution:

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture