Find the function The following limits represent the slope of a curve y=f(x) at the point {a,f(a)} Determine a possible function f and number a, then calculate the limitlim_{xrightarrow2}frac{5cdot x^2-20}{x-2}

EunoR 2021-02-26 Answered

Find the function The following limits represent the slope of a curve y=f(x) at the point {a,f(a)} Determine a possible function f and number a, then calculate the limit
limx25x220x2

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StrycharzT
Answered 2021-02-27 Author has 102 answers

Consider the given limit limx25x220x2
Note that, f(a)=limxaf(x)f(a)xa
That implies, f(x)=5x2 and a=2
Now obtain the limit as follows
limx25x220x2=limx25(x24)x2
=limx25(x222)x2
=limx25(x2)(x+2)(x2)
=limx25(x+2)
=5(2+2)
=54
=20
Hence, the value of the given limit is 20.

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