query: Using the defenition of a limit, show this: $\lim_{x\rightarrow a} f(x)= \lim_{h\rightarrow 0}f(a+h)$ when at least one of the two limits exist.
positive_passages.docid: 158152
positive_passages.text: Given $f: \Bbb R\rightarrow\Bbb R$ and a point $a\in\Bbb R$. Prove $lim_{x\rightarrow a} f(x)=\lim_{h\rightarrow 0} f(a+h)$ if 1 of the limits exists.
negative_passages.docid: 51594
negative_passages.text: $\lim_{n→∞} f(n+x)=0$ results in $ \lim_{x→∞} f(x)=0$
negative_passages.docid: 126256
negative_passages.text: Prove limit of function
negative_passages.docid: 10456
negative_passages.text: Finding limits $l=\lim_{x \rightarrow a}\frac{x^x-a^x}{x-a} $ & $m= \lim_{x \rightarrow a}\frac{a^x-x^a}{x-a} $.
negative_passages.docid: 95921
negative_passages.text: Question about $\lim _{q \rightarrow \infty}\|f\|_{q}=\|f\|_{\infty}$
negative_passages.docid: 32744
negative_passages.text: A clarification in a limit
negative_passages.docid: 57600
negative_passages.text: Show $\lim\limits_{a \rightarrow + \infty} \int_0^{\infty} \frac{1}{1+y^2}e^{-ay} dy =0 $
negative_passages.docid: 129579
negative_passages.text: If $f''(x_0)$ exists then $\lim_{x \to x_0} \frac{f(x_0+h)-2f(x_0)+f(x_0-h)}{h^2} = f''(x_0)$
negative_passages.docid: 133405
negative_passages.text: $\lim_{x \rightarrow 0} f'(x) = L$ exists, does it follow that $f'(0)$ exists?
negative_passages.docid: 12301
negative_passages.text: Show that $\lim_{n \rightarrow \infty} \sqrt[n]{a} =1$
negative_passages.docid: 6620
negative_passages.text: If $\lim\limits_{x\rightarrow\infty} (f'(x)+f(x)) =L<\infty$, does $\lim\limits_{x\rightarrow\infty} f(x) $ exist?
negative_passages.docid: 37489
negative_passages.text: Show that $ \lim_{(x,y) \to 0} \frac {|x|^ \alpha |y|^ \beta} {|x|^ \gamma + |y|^ \delta} \text {exists} \iff \alpha/\gamma + \beta/\delta > 1.$
negative_passages.docid: 20956
negative_passages.text: Correct way to prove the limit: $\mathop {\lim }\limits_{x \to 0} {x^\alpha }\int\limits_x^1 {\frac{{f\left( t \right)}}{{{t^{\alpha  + 1}}}}dt} $?
negative_passages.docid: 105569
negative_passages.text: If $f$ is integrable in $[a-1,b+1]$, then prove that $\lim \limits_{h\to 0} \ \int_{a}^{b}|f(x+h)-f(x)| ~ dx=0$
negative_passages.docid: 21879
negative_passages.text: Show that if $\lim_{x\to a}f'(x) = A$ then $f'(a)$ exists and equals A
negative_passages.docid: 1444
negative_passages.text: Prove/Show that Limit is equal to 0.
negative_passages.docid: 117246
negative_passages.text: Show that $\lim\limits_{a \to 0^+} \int^1_0 ax^{a−1}f(x)dx=f(0)$.