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If f(x)=∑k=1nxk\displaystyle f(x) = \sum_{k=1}^{n} x^k f(x)=k=1∑nxk, what is the value of limn→∞9n2+10n+11f′(1)?\displaystyle \lim_{n \to \infty} \frac{9n^2 + 10n + 11}{f'(1)} ?n→∞limf′(1)9n2+10n+11?
Evaluate limx→1x13+10x−11x−1\displaystyle \lim_{x \to 1} \frac{x^{13} + 10x-11}{x-1}x→1limx−1x13+10x−11.
If limx→0+(1+sin5x)cotx=a\displaystyle \lim_{x \to 0^+} (1+\sin 5 x)^{\cot x} = ax→0+lim(1+sin5x)cotx=a, what is the value of lna\ln alna?
Evaluate limx→01−cos(6x)x2\displaystyle \lim_{x \to 0} \frac{1 - \cos (6x)}{x^2}x→0limx21−cos(6x).
Evaluate limx→0+xlnx\displaystyle \lim_{x \to 0^+} x \ln x x→0+limxlnx.
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