Evaluate each limit if it exists. If the limit does not exist, explain why. Use the given graphs of f and g
(a) limx→2[f(x)+g(x)](b) limx→1[f(x)+g(x)](c) limx→0[f(x)g(x)](d) limx→−1f(x)g(x)(e) limx→2[x3f(x)](f) limx→2√3+f(x)
a.) limx→2[f(x)+g(x)]
limx→2[f(x)+g(x)]=limx→2f(x)+limx→2g(x)(Substitute the values of f(x) and g(x))limx→2[f(x)+g(x)]=2+0(Simplify)limx→2[f(x)+g(x)]=2
b.) limx→1[f(x)+g(x)]
limx→1[f(x)+g(x)]=limx→1f(x)+limx→1g(x)(Substitute the values of f(x) and g(x))limx→1f(x)=1limx→1g(x)=Does not existThe given equation does not exist because the left and the right limits of the function g(x) are different.
c.) limx→0[f(x)g(x)]
limx→0[f(x)g(x)]=limx→0f(x)⋅limx→0g(x)(Substitute the values of f(x) and g(x))limx→0[f(x)g(x)]=(0)(1.5)(Simplify)limx→0[f(x)g(x)]=0
d.) limx→−1f(x)g(x)
limx→−1f(x)g(x)=limx→−1f(x)limx→−1g(x)(Substitute the values of f(x) and g(x))limx→−1f(x)g(x)=−10(Does not exist)The limit does not exist, the function is undefined because the denominator is zero.
e.) limx→2[x3f(x)]
limx→2[x3f(x)]=limx→2x3⋅limx→2f(x)limx→2[x3f(x)]=(2)3(2)limx→2[x3f(x)]=16
f.) limx→2√3+f(x)
limx→2√3+f(x)(Substitute the value of f(x))limx→2√3+f(x)=√3+2(Simplify)limx→2√3+f(x)=√5
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