Find the indicated limit, if it exists.
@ganeshie8

Question

Find the indicated limit, if it exists.
@ganeshie8

anonymous · Answer

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anonymous · Answer

i only have like 2 questions that i would like to ask about (:

agreene · Answer

So, because you have a discontinuity you need to make sure your limit is valid by doing left and right limits. Because these are rather easy limits, and defined at 0 for the other two functions, you can just plug in and see what happens and see if that makes sense.
$$f(x)=7-x^2~~~~~~~~f(0)=7-0^2=7$$
$$f(x)=7-10x~~~~~~~~f(0)=7-10(0)=0$$
since we know y=7-x^2 is a parabola we know the limit will converge there, and since y=7-10x is linear we also know that the limit will exisit and is 7 as well, so the limit is 7 since the left and right limits agree

agreene · Answer

that 2nd set is supposed to be f(0) = 7-10(0) = 7         not 0

anonymous · Answer

gotcha! thanks!