Limits of Standard Functions
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Limits, Continuity and Differentiability

79572 \(\lim _{x \rightarrow 0} \frac{27^{x}-9^{x}-3^{x}+1}{\sqrt{5}-\sqrt{4+\cos x}}=\)

1 \(8 \sqrt{5}(\log 3)^{2}\)
2 \(\sqrt{5}(\log 3)^{2}\)
3 \(8 \sqrt{5} \log 3\)
4 \(16 \sqrt{5} \log 3\)
MHT CET-2022
Limits, Continuity and Differentiability

79573 \(\lim _{x \rightarrow 1} \frac{2^{2 x-2}-2^{x}+1}{\sin ^{2}(x-1)}\)

1 \(2 \log 2\)
2 \(\frac{1}{2}(\log 2)^{2}\)
3 \(2(\log 2)^{2}\)
4 \((\log 2)^{2}\)
MHT CET-2022
Limits, Continuity and Differentiability

79574 \(\lim _{x \rightarrow 2}\left(\frac{5 x-8}{\mathbf{8 - 3 x}}\right)^{\frac{3}{2 x-4}}=\)

1 \(\mathrm{e}^{3 / 2}\)
2 \(\mathrm{e}^{6}\)
3 \(\mathrm{e}^{2}\)
4 \(\mathrm{e}^{5 / 2}\)
MHT CET-2022
Limits, Continuity and Differentiability

79575 Letf \((x)=5-|x-2|\) and \(g(x)=|x+1|, x \in R\). If \(f(x)\) attains maximum value at \(\alpha\) and \(g(x)\) attains minimum value at \(\beta\) them \(\lim _{x \rightarrow-\alpha \beta} \frac{(x-1)\left(x^{2}-5 x+6\right)}{\left(x^{2}-6 x+8\right)}\) is equal to

1 \(-\frac{1}{2}\)
2 \(\frac{3}{2}\)
3 \(-\frac{3}{2}\)
4 \(\frac{1}{2}\)
MHT CET-2022
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Limits, Continuity and Differentiability

79572 \(\lim _{x \rightarrow 0} \frac{27^{x}-9^{x}-3^{x}+1}{\sqrt{5}-\sqrt{4+\cos x}}=\)

1 \(8 \sqrt{5}(\log 3)^{2}\)
2 \(\sqrt{5}(\log 3)^{2}\)
3 \(8 \sqrt{5} \log 3\)
4 \(16 \sqrt{5} \log 3\)
MHT CET-2022
Limits, Continuity and Differentiability

79573 \(\lim _{x \rightarrow 1} \frac{2^{2 x-2}-2^{x}+1}{\sin ^{2}(x-1)}\)

1 \(2 \log 2\)
2 \(\frac{1}{2}(\log 2)^{2}\)
3 \(2(\log 2)^{2}\)
4 \((\log 2)^{2}\)
MHT CET-2022
Limits, Continuity and Differentiability

79574 \(\lim _{x \rightarrow 2}\left(\frac{5 x-8}{\mathbf{8 - 3 x}}\right)^{\frac{3}{2 x-4}}=\)

1 \(\mathrm{e}^{3 / 2}\)
2 \(\mathrm{e}^{6}\)
3 \(\mathrm{e}^{2}\)
4 \(\mathrm{e}^{5 / 2}\)
MHT CET-2022
Limits, Continuity and Differentiability

79575 Letf \((x)=5-|x-2|\) and \(g(x)=|x+1|, x \in R\). If \(f(x)\) attains maximum value at \(\alpha\) and \(g(x)\) attains minimum value at \(\beta\) them \(\lim _{x \rightarrow-\alpha \beta} \frac{(x-1)\left(x^{2}-5 x+6\right)}{\left(x^{2}-6 x+8\right)}\) is equal to

1 \(-\frac{1}{2}\)
2 \(\frac{3}{2}\)
3 \(-\frac{3}{2}\)
4 \(\frac{1}{2}\)
MHT CET-2022
NEET DIGITAL LIBRARY
Limits, Continuity and Differentiability

79572 \(\lim _{x \rightarrow 0} \frac{27^{x}-9^{x}-3^{x}+1}{\sqrt{5}-\sqrt{4+\cos x}}=\)

1 \(8 \sqrt{5}(\log 3)^{2}\)
2 \(\sqrt{5}(\log 3)^{2}\)
3 \(8 \sqrt{5} \log 3\)
4 \(16 \sqrt{5} \log 3\)
MHT CET-2022
Limits, Continuity and Differentiability

79573 \(\lim _{x \rightarrow 1} \frac{2^{2 x-2}-2^{x}+1}{\sin ^{2}(x-1)}\)

1 \(2 \log 2\)
2 \(\frac{1}{2}(\log 2)^{2}\)
3 \(2(\log 2)^{2}\)
4 \((\log 2)^{2}\)
MHT CET-2022
Limits, Continuity and Differentiability

79574 \(\lim _{x \rightarrow 2}\left(\frac{5 x-8}{\mathbf{8 - 3 x}}\right)^{\frac{3}{2 x-4}}=\)

1 \(\mathrm{e}^{3 / 2}\)
2 \(\mathrm{e}^{6}\)
3 \(\mathrm{e}^{2}\)
4 \(\mathrm{e}^{5 / 2}\)
MHT CET-2022
Limits, Continuity and Differentiability

79575 Letf \((x)=5-|x-2|\) and \(g(x)=|x+1|, x \in R\). If \(f(x)\) attains maximum value at \(\alpha\) and \(g(x)\) attains minimum value at \(\beta\) them \(\lim _{x \rightarrow-\alpha \beta} \frac{(x-1)\left(x^{2}-5 x+6\right)}{\left(x^{2}-6 x+8\right)}\) is equal to

1 \(-\frac{1}{2}\)
2 \(\frac{3}{2}\)
3 \(-\frac{3}{2}\)
4 \(\frac{1}{2}\)
MHT CET-2022
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Limits, Continuity and Differentiability

79572 \(\lim _{x \rightarrow 0} \frac{27^{x}-9^{x}-3^{x}+1}{\sqrt{5}-\sqrt{4+\cos x}}=\)

1 \(8 \sqrt{5}(\log 3)^{2}\)
2 \(\sqrt{5}(\log 3)^{2}\)
3 \(8 \sqrt{5} \log 3\)
4 \(16 \sqrt{5} \log 3\)
MHT CET-2022
Limits, Continuity and Differentiability

79573 \(\lim _{x \rightarrow 1} \frac{2^{2 x-2}-2^{x}+1}{\sin ^{2}(x-1)}\)

1 \(2 \log 2\)
2 \(\frac{1}{2}(\log 2)^{2}\)
3 \(2(\log 2)^{2}\)
4 \((\log 2)^{2}\)
MHT CET-2022
Limits, Continuity and Differentiability

79574 \(\lim _{x \rightarrow 2}\left(\frac{5 x-8}{\mathbf{8 - 3 x}}\right)^{\frac{3}{2 x-4}}=\)

1 \(\mathrm{e}^{3 / 2}\)
2 \(\mathrm{e}^{6}\)
3 \(\mathrm{e}^{2}\)
4 \(\mathrm{e}^{5 / 2}\)
MHT CET-2022
Limits, Continuity and Differentiability

79575 Letf \((x)=5-|x-2|\) and \(g(x)=|x+1|, x \in R\). If \(f(x)\) attains maximum value at \(\alpha\) and \(g(x)\) attains minimum value at \(\beta\) them \(\lim _{x \rightarrow-\alpha \beta} \frac{(x-1)\left(x^{2}-5 x+6\right)}{\left(x^{2}-6 x+8\right)}\) is equal to

1 \(-\frac{1}{2}\)
2 \(\frac{3}{2}\)
3 \(-\frac{3}{2}\)
4 \(\frac{1}{2}\)
MHT CET-2022
For More Updates join with Us