Calculus

Limits of Sequences and Series

Properties of Limits

         

If sequence {an}\{a_n\} satisfies limn(2n1)an=16,\displaystyle \lim_{n \to \infty}(2n-1)a_n=16, what is the value of limnnan\displaystyle \lim_{n \to \infty}n a_n?

What is the value of limx05x(1x+115x+1)?\lim_{x \to 0} \frac{5}{x}\left(\frac{1}{x+1}-\frac{1}{5x+1}\right)?

Given that limn{an}=10 \displaystyle \lim_{n \to \infty} \left\{ a_n \right\} = 10 , and limn{bn}=11 \displaystyle \lim_{n \to \infty} \left\{ b_n \right\} = 11 , and {cn}={an+bn} \left\{ c_n \right\} = \left\{ a_n + b_n \right\} , evaluate: limn{cn}. \displaystyle \lim_{n \to \infty} \left\{ c_n \right\}.

Below is the graph of y=f(x),y=f(x), with a=5a=5, b=2b=2 and c=9c=9. What is the value of limxa+f(x)+limxaf(x)?\lim_{x \to a^+} f(x)+\lim_{x \to a^-} f(x)?

Below is the graph of function f(x).f(x). If a=10,b=20,f(a)=c=10,a=10, b=20, f(a)=c=10, what is the value of limxaf(x)?\displaystyle \lim_{x \to a} f(x)?

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