1.What is the mathematical notation for the Left Hand Limit (LHL) at $x = a$?
2.What is the mathematical notation for the Right Hand Limit (RHL) at $x = a$?
3.For a limit to exist at $x = a$, the LHL must be equal to ________.
4.Complete the condition for continuity at $x = a$: $\text{LHL} = \text{RHL} = $ ________.
5.Evaluate: $\lim_{x \to 3} (2x + 1)$.
6.Evaluate: $\lim_{x \to 0} \sin x$.
7.Evaluate: $\lim_{x \to 1} (x^2 - 1)$.
8.True or False: A constant function $f(x) = 5$ is continuous everywhere.
9.True or False: Every polynomial function is continuous for all real numbers.
10.At which specific point is $f(x) = \frac{1}{x}$ discontinuous?
11.What is the derivative of any constant number (like $7$ or $\pi$)?
12.Write the Power Rule: $\frac{d}{dx}(x^n) = $ ________.
13.Find the derivative of $y = x$.
14.Find the derivative of $y = x^2$.
15.Find the derivative of $y = x^5$.
16.Find the derivative of $y = \sqrt{x}$ (i.e., $x^{1/2}$).
17.Find the derivative of $y = \frac{1}{x}$ (i.e., $x^{-1}$).
18.$\frac{d}{dx}(\sin x) = $ ________.
19.$\frac{d}{dx}(\cos x) = $ ________.
20.$\frac{d}{dx}(\tan x) = $ ________.
21.$\frac{d}{dx}(\cot x) = $ ________.
22.$\frac{d}{dx}(\sec x) = $ ________.
23.$\frac{d}{dx}(\text{cosec } x) = $ ________.
24.Find the derivative of $y = 3x^4$.
25.Find the derivative of $y = x^2 + \sin x$.
26.Find the derivative of $y = 5x - 2$.
27.Complete the Product Rule: $\frac{d}{dx}(u \cdot v) = u \cdot \frac{dv}{dx} + $ ________.
28.Complete the Quotient Rule denominator: $\frac{d}{dx}\left(\frac{u}{v}\right) = \frac{v \cdot u' - u \cdot v'}{\text{?}}$.
29.Complete the Chain Rule: $\frac{dy}{dx} = \frac{dy}{dt} \times $ ________.
30.Apply Chain Rule: Find $\frac{d}{dx}(\sin(2x))$.
31.Apply Chain Rule: Find $\frac{d}{dx}(\cos(3x))$.
32.Apply Chain Rule: Find $\frac{d}{dx}(e^{5x})$.
33.Apply Chain Rule: Find $\frac{d}{dx}(2x+1)^2$.
34.Apply Chain Rule: Find $\frac{d}{dx}(\tan(4x))$.
35.Apply Product Rule: Find the derivative of $x \cdot e^x$.
36.Apply Product Rule: Find the derivative of $x \cdot \sin x$.
37.Apply Quotient Rule setup: If $y = \frac{x}{\sin x}$, what is $u$ and what is $v$?
38.What is the derivative of $y$ with respect to $x$?
39.Using the chain rule, what is the derivative of $y^2$ with respect to $x$?
40.Using the chain rule, what is the derivative of $\sin y$ with respect to $x$?
41.If $x + y = 10$, find $\frac{dy}{dx}$.
42.If $2x + 3y = \sin x$, find $\frac{dy}{dx}$.
43.$\frac{d}{dx}(\sin^{-1}x) = $ ________.
44.$\frac{d}{dx}(\cos^{-1}x) = $ ________.
45.$\frac{d}{dx}(\tan^{-1}x) = $ ________.
46.$\frac{d}{dx}(\cot^{-1}x) = $ ________.
47.$\frac{d}{dx}(\sec^{-1}x) = $ ________.
48.$\frac{d}{dx}(\text{cosec}^{-1}x) = $ ________.
49.$\frac{d}{dx}(e^x) = $ ________.
50.$\frac{d}{dx}(\log_e x) = $ ________.
51.$\frac{d}{dx}(a^x) = $ ________.
52.Find the derivative of $e^{-x}$.
53.Find the derivative of $2^x$.
54.Find the derivative of $\log(2x)$.
55.Log Property: $\log(a \cdot b) = $ ________.
56.Log Property: $\log\left(\frac{a}{b}\right) = $ ________.
57.Log Property: $\log(m^n) = $ ________.
58.To differentiate $x^x$, what is the very first step?
59.If $x = f(t)$ and $y = g(t)$, complete the formula: $\frac{dy}{dx} = \frac{\text{?}}{\frac{dx}{dt}}$.
60.If $x = 2t$, find $\frac{dx}{dt}$.
61.If $y = 3t^2$, find $\frac{dy}{dt}$.
62.Using the values from Q60 and Q61, find $\frac{dy}{dx}$.
63.If $y = f(x)$, what symbol is used for the "Second Order Derivative"?
64.If $y = x^2$, what is $\frac{dy}{dx}$?
65.Continuing from Q64, what is the second derivative $\frac{d^2y}{dx^2}$?
66.If $y = x^3$, find $\frac{d^2y}{dx^2}$.
67.If $y = 5x$, find $\frac{d^2y}{dx^2}$.
68.If $y = e^x$, find $\frac{d^2y}{dx^2}$.
69.For Rolle's Theorem, the function must be continuous on the ________ interval $[a, b]$.
70.For Rolle's Theorem, the function must be differentiable on the ________ interval $(a, b)$.
71.What is the third condition required for Rolle's Theorem regarding $f(a)$ and $f(b)$?
72.If Rolle's Theorem holds, then there exists at least one point $c$ such that $f'(c) = $ ________.
73.Does Lagrange's Mean Value Theorem (LMVT) require $f(a) = f(b)$?
74.If LMVT holds, then $f'(c) = \frac{f(b) - f(a)}{\text{?}}$.
75.Geometrically, $f'(c)=0$ in Rolle's Theorem means the tangent is parallel to the ________ axis.
