Answer:
Limits
If
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Let
. Show that
does not exist.
Answer:
Let
. Show that
does not exist.
Answer:
Let
. Show that
does not exist.
Answer:
Let
. Show that
does not exist.
Answer:
Let
Find ![Rendered by QuickLaTeX.com \begin{array}{l} \mathop {\lim }\limits_{x \to 1} f(x) \end{array}](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-0547da0e41bd33f432cec4b994fa8af2_l3.png)
Answer:
Let
Find ![Rendered by QuickLaTeX.com \begin{array}{l} \mathop {\lim }\limits_{x \to 2} f(x) \end{array}](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-f3045f827c1a1b5b44e0c8aac5f68a01_l3.png)
Answer:
Let
Show that
does not exist.
Answer:
Evaluate the following limits: ![Rendered by QuickLaTeX.com \mathop {\lim }\limits_{x \to 0} \frac{{\sin (x/4)}}{{x}}](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-9fa4c9fcdba716d72c954235e140de84_l3.png)
Answer:
Evaluate the following limits: ![Rendered by QuickLaTeX.com \mathop {\lim }\limits_{x \to 0} \frac{{\sin x cos x}}{{3x}}](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-a2976a4d6aa659e8121f2edb2b43d5a9_l3.png)
Answer:
Evaluate the following limits: ![Rendered by QuickLaTeX.com \mathop {\lim }\limits_{x \to 0} (x\cot 2x)](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-d368cc4ae51f51bd4fa5861481ecc836_l3.png)
Answer:
Evaluate the following limits: ![Rendered by QuickLaTeX.com \mathop {\lim }\limits_{x \to 0} x{\mathop{\rm cosec}\nolimits} x](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-054be83acd9318a5b649a803b63f9f37_l3.png)
Answer:
Evaluate the following limits: ![Rendered by QuickLaTeX.com \mathop {\lim }\limits_{x \to 0} \frac{{\tan x - \sin x}}{{{{\sin }^3}x}}](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-4b1bc4ef2480bbe2e70cc3f70b8a0b50_l3.png)
Answer:
Evaluate the following limits: ![Rendered by QuickLaTeX.com \mathop {\lim }\limits_{x \to 0} \frac{{x\cos x + \sin x}}{{{x^2} + \tan x}}](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-fb88f9abdc9565267a813d6b88ec8fc0_l3.png)
Answer:
Evaluate the following limits: ![Rendered by QuickLaTeX.com \mathop {\lim }\limits_{x \to 0} \frac{{({x^2} - \tan 2x)}}{{\tan x}}](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-98223c2354252ee5e0abde84d2635188_l3.png)
Answer:
Evaluate the following limits: ![Rendered by QuickLaTeX.com \mathop {\lim }\limits_{x \to 0} \frac{{\(tan2x - x)}}{{(3x - tanx)}}](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-e8df34b9da78aaabc621c45f21bef8c5_l3.png)
Answer:
Evaluate the following limits: ![Rendered by QuickLaTeX.com \mathop {\lim }\limits_{x \to 0} \frac{{\sin 2x + 3x}}{{2x + sin3x}}](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-439b3d345f579268b7707ae1f7b89376_l3.png)
Answer:
Evaluate the following limits:
\pi
6![Rendered by QuickLaTeX.com }}} \frac{{(2{{\sin }^2}x + \sin x - 1)}}{{(2{{\sin }^2}x - 3\sin x + 1)}}](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-3187ea247d578f21f36a05b8848174c9_l3.png)
Answer:
Evaluate the following limits: ![Rendered by QuickLaTeX.com \mathop {\lim }\limits_{x \to 0} \frac{{\sinx - 2sin3x + sin5x}}{{x}}](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-c60bb8307fe5ad9cc523aa45a9f7b138_l3.png)
Answer:
Evaluate the following limits: ![Rendered by QuickLaTeX.com \mathop {\lim }\limits_{x \to 0} \frac{{\sin mx}}{{tan nx}}](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-5ddd1a80e0a5ad72700905509a44f626_l3.png)
Answer:
Evaluate the following limits: ![Rendered by QuickLaTeX.com \mathop {\lim }\limits_{x \to 0} \frac{{\tan 3x}}{{sin 4x}}](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-7808469936be72d321b132fc291e1c59_l3.png)
Answer:
Evaluate the following limits: ![Rendered by QuickLaTeX.com \mathop {\lim }\limits_{x \to 0} \frac{{\sin 4x}}{{tan 7x}}](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-81ed4eba641735727d5fca71f4661b55_l3.png)
Answer:
Evaluate the following limits: ![Rendered by QuickLaTeX.com \mathop {\lim }\limits_{x \to 0} \frac{{\tan \alpha x}}{{\tan \beta x}}](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-21eda64cd89a192ad9897e431db12b00_l3.png)
Answer:
Evaluate the following limits: ![Rendered by QuickLaTeX.com \mathop {\lim }\limits_{x \to 0} \frac{{\tan 3x}}{{tan 5x}}](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-0461dc6a88d6eda370e9aa557488a576_l3.png)
Answer:
Evaluate the following limits: ![Rendered by QuickLaTeX.com \mathop {\lim }\limits_{x \to 0} \frac{{\sin 5x}}{{sin 8x}}](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-b891b320b95fc24691e80cc34f8d4634_l3.png)
Answer:
Evaluate the following limits: ![Rendered by QuickLaTeX.com \mathop {\lim }\limits_{x \to 0} \frac{{\sin 4x}}{{6x}}](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-b756502266fbd495c3127c0bc7f97175_l3.png)
Answer:
Evaluate ![Rendered by QuickLaTeX.com \mathop {\lim }\limits_{x \to a} \left( {\frac{{\sqrt x - \sqrt a }}{{x - a}}} \right)](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-fa99f3ba3757cc5b71b1d47752a203cf_l3.png)
Answer:
Evaluate ![Rendered by QuickLaTeX.com \mathop {\lim }\limits_{h \to 0} \left( {\frac{{\sqrt x+h - \sqrt x }}{h} \right)](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-e2d20a68ef3ca95cf72a328b87c5c498_l3.png)
Answer:
Evaluate ![Rendered by QuickLaTeX.com \mathop {\lim }\limits_{h \to 0} \frac{1}{h}\left\{ {\frac{1}{{\sqrt {x + h} }} - \frac{1}{{\sqrt x }}} \right\}](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-b1d241665963a097de1f1157d52d1fe7_l3.png)
Answer:
Evaluate ![Rendered by QuickLaTeX.com \mathop {\lim }\limits_{x \to 0} \left( {\frac{{\sqrt {1 + x} - 1}}{x}} \right)](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-fec3541f8299acaa05c29d55f6d391dc_l3.png)
Answer:
Evaluate ![Rendered by QuickLaTeX.com \mathop {\lim }\limits_{x \to 0} \left( {\frac{{\sqrt {2 - x} - \sqrt {2 + x} }}{x}} \right)](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-f27bdbb07b60a3ada0495d793a81926d_l3.png)
Answer:
Evaluate ![Rendered by QuickLaTeX.com \mathop {\lim }\limits_{x \to 2} (5 - x)](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-fb0a898f79bd677837676a0ea53769fb_l3.png)
Answer:
Evaluate ![Rendered by QuickLaTeX.com \mathop {\lim }\limits_{x \to 1} (6{x^2} - 4x + 3)](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-3081cdbfa977a74fa6dc78920185f782_l3.png)
Answer:
Evaluate ![Rendered by QuickLaTeX.com \mathop {\lim }\limits_{x \to 3} \left( {\frac{{{x^2} + 9}}{{x + 3}}} \right)](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-51d3534a32946849e91fa95b69ef04d1_l3.png)
Answer:
Evaluate ![Rendered by QuickLaTeX.com \mathop {\lim }\limits_{x \to 3} \left( {\frac{{{x^2} - 4x}}{{x - 2}}} \right)](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-d11da59495965e8cd99f3873c6265e9b_l3.png)
Answer:
Evaluate ![Rendered by QuickLaTeX.com \mathop {\lim }\limits_{x \to 5} \left( {\frac{{{x^2} - 25}}{{x - 5}}} \right)](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-49b9470d24c59a2732fdb4ec15a72d59_l3.png)
Answer:
Evaluate ![Rendered by QuickLaTeX.com \mathop {\lim }\limits_{x \to 1} \left( {\frac{{{x^3} - 1}}{{x - 1}}} \right)](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-f61140ceeefc27238a2ee20da858060e_l3.png)
Answer:
Evaluate ![Rendered by QuickLaTeX.com \mathop {\lim }\limits_{x \to -2} \left( {\frac{{{x^3} + 8}}{{x + 2}}} \right)](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-5d9ca1670d4cba8b0ef1417d1cae4def_l3.png)
Answer:
Evaluate ![Rendered by QuickLaTeX.com \mathop {\lim }\limits_{x \to 3} \left( {\frac{{{x^4} - 81}}{{x - 3}}} \right)](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-6e21f8d90b2cfe44f17d6952cb85a735_l3.png)
Answer:
Evaluate ![Rendered by QuickLaTeX.com \mathop {\lim }\limits_{x \to 3} \left( {\frac{{{x^2} - 4x + 3}}{{{x^2} - 2x - 3}}} \right)](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-98942250a35680da7cc823fcf3e9e6fb_l3.png)
Answer:
Evaluate ![Rendered by QuickLaTeX.com \mathop {\lim }\limits_{x \to \frac{1}{2}} \left( {\frac{{4{x^2} - 1}}{{2x - 1}}} \right)](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-fd1680c7566a07e336c8805c52939fc4_l3.png)
Answer:
Evaluate ![Rendered by QuickLaTeX.com \mathop {\lim }\limits_{x \to \ 4} \left( {\frac{{{x^3} - 64}}{{{x^2} - 16}}} \right)](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-844f9dff3e3d8e11099c8bf10c6d218b_l3.png)
Answer:
Evaluate ![Rendered by QuickLaTeX.com \mathop {\lim }\limits_{x \to \ 2} \left( {\frac{{{x^5} - 32}}{{{x^3} - 8}}} \right)](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-79a4bebc2a68f4836b3f4cedd2120c27_l3.png)
Answer:
Evaluate ![Rendered by QuickLaTeX.com \mathop {\lim }\limits_{x \to a} \left( {\frac{{{x^{\frac{5}{2}}} - {a^{\frac{5}{2}}}}}{{x - a}}} \right)](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-de06ef03063cfe0d755ed271bd9c99ce_l3.png)
Answer:
Evaluate ![Rendered by QuickLaTeX.com \mathop {\lim }\limits_{x \to a} \left( {\frac{{{(x+2)^{\frac{5}{2}}} - {(a+2)^{\frac{5}{2}}}}}{{x - a}}} \right)](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-2082b749fc53a8c67d77b8a6bc755dd6_l3.png)
Answer:
Evaluate ![Rendered by QuickLaTeX.com \mathop {\lim }\limits_{x \to 1} \left( {\frac{{{x^n} - 1}}{{ x - 1}}} \right)](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-b91e743bd5034ea9be9b4e8e5abd6067_l3.png)
Answer: