this is a problem from my worksheet that i cant figure out how to simplify. also i can't figure out lim x->16 sqrt x -4/x-16 *the square root is only for the x.
Thanks in advance! (:
Thanks in advance! (:
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lim x->4 for (h+2)^2-9h/h-4
take derivative for top and bottom. The derivative of the denominator is 1.
Derivative of numerator is
f(h) = (h + 2)² - 9h
f'(h) = 2(h + 2) - 9
so lim x->4 for (h+2)^2-9h/h-4
= lim x-->4 of 2(h + 2) - 9 = 3
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Second problem can be solve by taking derivative or using this method.
x - 16 = (√x)² - 4² = (√x - 4)(√x + 4)
You see that (√x - 4) cancel out so you only need to solve
lim x--> 16 of 1/(√x + 4) = 1/8
take derivative for top and bottom. The derivative of the denominator is 1.
Derivative of numerator is
f(h) = (h + 2)² - 9h
f'(h) = 2(h + 2) - 9
so lim x->4 for (h+2)^2-9h/h-4
= lim x-->4 of 2(h + 2) - 9 = 3
---------------------------------
Second problem can be solve by taking derivative or using this method.
x - 16 = (√x)² - 4² = (√x - 4)(√x + 4)
You see that (√x - 4) cancel out so you only need to solve
lim x--> 16 of 1/(√x + 4) = 1/8