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77-82 Find the limit by interpreting the expression as an appropriate derivative. $e^{3x} - 1$ 77. $\lim_{x \to 0} \frac{e^{3x} - 1}{x}$ $10^h - 1$ 79. $\lim_{h \to 0} \frac{10^h - 1}{h}$ $9 \left[ \sin^{-1} \left( \frac{\sqrt{3}}{2} + \Delta x \right) \right]^2 - \pi^2$ 81. $\lim_{\Delta x \to 0} \frac{9 \left[ \sin^{-1} \left( \frac{\sqrt{3}}{2} + \Delta x \right) \right]^2 - \pi^2}{\Delta x}$ $3 \sec^{-1} w - \pi$ 82. $\lim_{w \to 2} \frac{3 \sec^{-1} w - \pi}{w - 2}$ $exp(x^2) - 1$ 78. $\lim_{x \to 0} \frac{exp(x^2) - 1}{x}$ $\tan^{-1}(1 + h) - \pi/4$ 80. $\lim_{h \to 0} \frac{\tan^{-1}(1 + h) - \pi/4}{h}$

          77-82 Find the limit by interpreting the expression as an appropriate derivative.
$e^{3x} - 1$
77. $\lim_{x \to 0} \frac{e^{3x} - 1}{x}$
$10^h - 1$
79. $\lim_{h \to 0} \frac{10^h - 1}{h}$
$9 \left[ \sin^{-1} \left( \frac{\sqrt{3}}{2} + \Delta x \right) \right]^2 - \pi^2$
81. $\lim_{\Delta x \to 0} \frac{9 \left[ \sin^{-1} \left( \frac{\sqrt{3}}{2} + \Delta x \right) \right]^2 - \pi^2}{\Delta x}$
$3 \sec^{-1} w - \pi$
82. $\lim_{w \to 2} \frac{3 \sec^{-1} w - \pi}{w - 2}$ 
$exp(x^2) - 1$
78. $\lim_{x \to 0} \frac{exp(x^2) - 1}{x}$
$\tan^{-1}(1 + h) - \pi/4$
80. $\lim_{h \to 0} \frac{\tan^{-1}(1 + h) - \pi/4}{h}$

77-82 Find the limit by interpreting the expression as an appropriate derivative.
e^3x - 1
77. limx → 0(e^3x - 1)/(x)
10^h - 1
79. limh → 0(10^h - 1)/(h)
9 [ sin^-1( (√(3))/(2) + Δ x ) ]^2 - π^2
81. limΔ x → 0(9 [ sin^-1( (√(3))/(2) + Δ x ) ]^2 - π^2)/(Δ x)
3 sec^-1 w - π
82. limw → 2(3 sec^-1 w - π)/(w - 2)
exp(x^2) - 1
78. limx → 0(exp(x^2) - 1)/(x)
tan^-1(1 + h) - π/4
80. limh → 0(tan^-1(1 + h) - π/4)/(h)

Added by Anna K.

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