Suppose that
limx→af(x)=0limx→alimx→ah(x)=1
limx→ap(x)=∞limx→aq(x)=∞
Which of the following limits are indeterminate form? Evaluate the limit if possible, for those that are not an indefinite form.
a.) limx→a[f(x)]g(x)
b.) limx→a[f(x)]p(x)
c.) limx→a[h(x)]p(x)
d.) limx→a[p(x)]f(x)
e.) limx→a[p(x)]q(x)
f.) limx→aq(x)√p(x)
a. ) limx→a[f(x)]g(x)=limx→a[f(x)]limx→ag(x)=00⟸(Indeterminate)b. ) limx→a[f(x)]p(x)=limx→a[f(x)]limx→ap(x)=0∞=0c. ) limx→a[h(x)]p(x)=limx→a[h(x)]limx→ap(x)=1∞⟸(Indeterminate)d. ) limx→a[p(x)]f(x)=limx→a[p(x)]limx→af(x)=∞0⟸(Indeterminate)e. ) limx→a[p(x)]q(x)=limx→a[p(x)]limx→aq(x)=∞∞=∞e. ) limx→aq(x)√p(x)=limx→a[p(x)]1q(x)=limx→a[p(x)]1limx→aq(x)=∞1∞=∞0⟸(Indeterminate)
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