Sonia Ayers
2022-07-02
Answered

The mad hatter wishes to by some cases of tea. He has 200 gold coins and a case of 500 tea bags costs 15 gold coins. How many cases of tea can he buy?

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asked 2021-12-06

Find the limits in Exercises 51-66.

51.$\underset{x\Rightarrow {1}^{+}}{lim}{x}^{\frac{1}{1-x}}$ 52. $\underset{x\Rightarrow {1}^{+}}{lim}{x}^{\frac{1}{1-x}}$

53.$\underset{x\Rightarrow \mathrm{\infty}}{lim}{\left(\mathrm{ln}x\right)}^{\frac{1}{x}}$ 54. $\underset{x\Rightarrow {e}^{+}}{lim}{\left(\mathrm{ln}x\right)}^{\frac{1}{x-e}}$

55.$\underset{x\Rightarrow {0}^{+}}{lim}{x}^{-\frac{1}{\mathrm{ln}x}}$ 56. $\underset{x\Rightarrow \mathrm{\infty}}{lim}{x}^{\frac{1}{\mathrm{ln}x}}$

57.$\underset{x\Rightarrow \mathrm{\infty}}{lim}{(1+2x)}^{\frac{1}{2\mathrm{ln}x}}$ 58. $\underset{x\Rightarrow 0}{lim}{({e}^{x}+x)}^{\frac{1}{x}}$

59.$\underset{x\Rightarrow {0}^{+}}{lim}{x}^{x}$ 60. $\underset{x\Rightarrow {0}^{+}}{lim}{(1+\frac{1}{x})}^{x}$

61.$\underset{x\Rightarrow 0}{lim}{\left(\frac{x+2}{x-1}\right)}^{x}$ 62. $\underset{x\Rightarrow \mathrm{\infty}}{lim}{\left(\frac{{x}^{2}+1}{x+2}\right)}^{\frac{1}{x}}$

63.$\underset{x\Rightarrow {0}^{+}}{lim}{x}^{2}\mathrm{ln}x$ 64. $\underset{x\Rightarrow {0}^{+}}{lim}x{\left(\mathrm{ln}x\right)}^{2}$

65.$\underset{x\Rightarrow {0}^{+}}{lim}x\mathrm{tan}(\frac{\pi}{2}-x)$ 66. $\underset{x\Rightarrow {0}^{+}}{lim}\mathrm{sin}x\cdot \mathrm{ln}x$

51.

53.

55.

57.

59.

61.

63.

65.

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Table shows the number of cellular phone subscribers in the United States and their average monthly bill in the years from 2000 to 2010.

One of the scatter plots clearly suggests a linear model. Use the points at

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Evaluate the expression ans write the result in theform a + bi

$\frac{1-\sqrt{-1}}{1+\sqrt{-1}}$

$\frac{1-\sqrt{-1}}{1+\sqrt{-1}}$

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How do you express the phrase "Twelve less a number is 40" as an algebraic expression?