Evaluate \displaystyle \lim_{x \to 0}

Evaluate \displaystyle \lim_{x \to 0} \frac{e^{44x} - 1}{x^2+2x}.
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Given f(x) = x^4 + 6x^3 - 15x + 7, evaluate \displaystyle \lim_{h \to 0} \frac{f(1+h) - f(1-h)}{h}.
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Consider the general case where the two classes have different means and possibly different variances:\displaystyle
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Given two data points in 2 dimensions:\displaystyle \displaystyle \mathbf{x}^{(1)} \displaystyle = \displaystyle (x^{(1)},
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Given two data points in 2 dimensions:\displaystyle \displaystyle \mathbf{x}^{(1)} \displaystyle = \displaystyle (x^{(1)},
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Evaluate \displaystyle \lim_{x \to 0} \frac{\sqrt{2}x}{\sqrt{2+x}-\sqrt{2}}.
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Consider the same statistical set-up as above. Suppose we observe a data set consisting of 1000 observations as described in the
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Recall from the slides that the Gamma distribution can be reparameterized using the two parameters a, the shape parameter, and
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2. 140 views
For the two following pmfs with one parameter \theta that are written in the form\displaystyle \displaystyle f_\theta (y)
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a and b are integers that satisfy: \displaystyle \lim_{x \to 1} \frac{x-1}{x^2-ax+b} = -\frac{1}{3}. What is the value of a+b?
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