Calculus 1

What is the indefinite integral of $y = 100x^2$

$\lim_{x \to 3} (2x + 5)$

$\lim_{t \rightarrow 1} \frac{t^3 - t}{t^2 - 1}$

$\lim_{h\rightarrow 0} \frac{(h-5)^2 - 25}{h}$

Use the squeeze theorem to prove the following important trigonometric limit

$\lim_{\theta\rightarrow 0} \frac{\sin(\theta)}{\theta} = 1$

$\lim_{x\rightarrow \infty}\frac{2x - 1}{x + 1}$

$\lim_{\rightarrow \infty}\sin\frac{1}{x}$

$\lim_{\theta\rightarrow 0} \frac{\sec{(2\theta)} \tan{(3 \theta)}}{5 \theta}$

$\lim_{x\rightarrow 0} \frac{\tan{x}}{x}$

Compute $f'(x)$ using the limit definition of the derivative $f'(a) = \lim_{h \to 0} \frac{f(a+h) - f(a)}{h}$ for the following 1. f(x) = 3 2. f(x) = 3x-1 3. f(x) = $x^2 + x$ 4. f(x) = $\sqrt(x)$ 5. f(x) = 1/x

Use the definition of derivatives to find the derivative of the following function,

$f(x) = \sqrt{x - 1}$

Use the definition of the derivative to find $f\prime(x)$ if

$f(x) = \frac{2}{3 - 5x}$

Find the derivative of $f(x) = \sin{x}(x^2 + 5)$

Use the power rule to find the derivative of $f(x) = 2x^5$

Use the power rule to find the derivative of $f(x) = 2x^{\frac{3}{2}}$

Using the power rule for derivatives, find the first derivative of the function,

$f(x) = \frac{4}{x^3}$

Use the product rule to find the derivative of $y = 5x(x^2 - 2)$

Find the derivative of $2^{3x} \cdot 5^{4x^2}$

Use the definition of the derivative to show that the derivative of $\sin{x}$ is equal to $\cos{x}$

Show that the derivative of $\cos{x}$ is equal to $-\sin{x}$