find lim, x->4, f(x), given -x+10<=f(x)<=x^2-9x+26; use algebra to simplify diff....

[hec07]

find lim, x->4, f(x), given -x+10<=f(x)<=x^2-9x+26; use algebra to simplify diff....

1. Suppose:

. . . . .\(\displaystyle -x\, +\, 10\, \leq\, f(x)\, \leq\, x^2\, -\,9x\, +\, 26\)

Use this to compute the following limit:

. . . . .\(\displaystyle \displaystyle \lim_{x \rightarrow 4}\, f(x)\)

2. Evaluate the limit below in two steps by using algebra to simplify the difference quotient and then evaluating the limit:

. . . . .\(\displaystyle \displaystyle \lim_{h \rightarrow 0^+}\, \dfrac{\sqrt{\strut h^2\, +\, 15h\, +\, 5\, }\, -\, \sqrt{\strut 5\,}}{h}\)

 

[ksdhart2]

What have you tried? What are your thoughts? For instance on the first (left) problem, you evaluated the bounds on the limit by plugging x=4 into the left side and right sides of the given inequality, and... then what? And on the second (right) problem, you multiplied by the conjugate, and... then what? Please share with us any and all work you've done on this problem, even the parts you know are wrong. Thank you.