Objective Questions - MTH 102

Questions (105)

#	Question	Topic	Actions
1	When evaluating the limit of \( f(x) = \frac{7 + x}{9 - x} \) as \( x \) approa…	Limits	View
2	Which of the following is considered an indeterminate form that requires furthe…	Limits	View
3	What is the limit of \( x^2 + 3 \) as \( x \) tends to 2?	Limits	View
4	Why can the limit of \( \frac{x(x+1)}{x} \) as \( x \) tends to 0 not be evalua…	Limits	View
5	According to the properties of limits, the limit of a sum \( [f(x) + g(x)] \) i…	Limits	View
6	Evaluate the limit of \( \frac{3x^3 + 4x^2 + 2x}{x^2 + 5x} \) as \( x \) tends …	Limits	View
7	Evaluate the limit of \( \frac{x^3 - 8}{x^2 - 4} \) as \( x \) tends to 2.	Limits	View
8	What is the result of dividing any non-zero number by infinity \( \left( \frac{…	Limits	View
9	In the rationalisation method for limits involving square roots, what is the co…	Limits	View
10	Evaluate the limit of \( \frac{\sqrt{x} - 1}{x - 1} \) as \( x \) tends to 1.	Limits	View
11	Evaluate the limit of \( \frac{x - 1}{\sqrt{x^2 + 3} - 2} \) as \( x \) tends t…	Limits	View
12	When evaluating a limit as \( x \) approaches infinity for a rational function,…	Limits	View
13	Evaluate the limit of \( \frac{2x^4 - 3x^2 + 1}{6x^4 + x^3 - 3x} \) as \( x \) …	Limits	View
14	What is the value of the trigonometric limit: \( \lim_{x \to 0} \frac{\sin x}{x…	Limits	View
15	What is the value of the trigonometric limit: \( \lim_{x \to 0} \frac{\tan x}{x…	Limits	View
16	L'Hospital's Rule can be applied when the limit of \( \frac{f(x)}{g(x)} \) resu…	Limits	View
17	Evaluate the limit of \( \frac{\cos x - 1}{x} \) as \( x \) approaches 0.	Limits	View
18	Evaluate the limit of \( \frac{\tan x}{\sin 2x} \) as \( x \) approaches \( \pi…	Limits	View
19	Evaluate the limit of \( x^2 + 2x + 5 \) as \( x \) tends to 3.	Limits	View
20	Evaluate the limit of \( \frac{x^2 - 4}{x^2 + x - 6} \) as \( x \) tends to 2.	Limits	View
21	Evaluate the limit of \( \frac{4x^2 + 3x - 1}{2x^2 + x - 2} \) as \( x \) tends…	Limits	View
22	Evaluate the limit of \( \frac{4x^2 + 2x - 1}{3x^2 + x - 2} \) as \( x \) tends…	Limits	View
23	Evaluate the limit of \( \frac{(x + 1)(2x + 1)(x - 3)}{x^3} \) as \( x \) tends…	Limits	View
24	What is the limit of \( \frac{1 - \cos x}{x} \) as \( x \) tends to 0?	Limits	View
25	Evaluate the limit of \( \frac{\tan 3x}{x} \) as \( x \) tends to 0.	Limits	View
26	What is the limit of \( \frac{\sqrt{x + h} - \sqrt{x}}{h} \) as \( h \) tends t…	Limits	View
27	Evaluate the limit of \( \frac{\sqrt{x^2 + 9} - 3}{x^2} \) as \( x \) tends to …	Limits	View
28	Evaluate the limit of \( \frac{3x^2 - 12}{x - 2} \) as \( x \) tends to 2.	Limits	View
29	According to the provided formulas, what is the limit of \( \frac{1 - \cos ax}{…	Limits	View
30	Evaluate the limit of \( \frac{x^2 + x - 2}{x - 1} \) as \( x \) tends to 1.	Limits	View
31	Evaluate the limit of \( \frac{e^{x-1} - x}{(x - 1)^2} \) as \( x \) tends to 1.	Limits	View
32	Evaluate the limit of \( \frac{e^{3x}}{x^2} \) as \( x \) tends to infinity.	Limits	View
33	Evaluate the limit of \( \frac{\ln(1 + x^{-1})}{x^{-1}} \) as \( x \) tends to …	Limits	View
34	Evaluate the limit of \( \frac{\ln x}{\sqrt{x}} \) as \( x \) tends to infinity.	Limits	View
35	Evaluate the limit of \( \frac{1 - x + \ln x}{x^3 - 3x + 2} \) as \( x \) tends…	Limits	View
36	Evaluate the limit of \( \frac{\ln(2 + e^x)}{3x} \) as \( x \) tends to infinit…	Limits	View
37	Evaluate the limit of \( \frac{x^3 - x^2 - x - 2}{x^3 - 8} \) as \( x \) tends …	Limits	View
38	Evaluate the limit of \( \frac{x^2 - x - 6}{x^2 - 9} \) as \( x \) tends to 3.	Limits	View
39	Evaluate the limit of \( \frac{x - 4}{\sqrt{x} - 2} \) as \( x \) tends to 4.	Limits	View
40	What is the limit of \( \frac{x^3 - 6x + 2}{x^2 + x + 9} \) as \( x \) approach…	Limits	View
41	Evaluate the limit of \( \frac{(x-2)^3 + 8}{x} \) as \( x \) approaches 0.	Limits	View
42	Evaluate the limit of \( \frac{(x-2)(x^2 + 3x - 2)}{x^2 - 4} \) as \( x \) appr…	Limits	View
43	Evaluate the limit of \( \frac{x^2 + a^2}{x^3 + a^3} \) as \( x \) tends to inf…	Limits	View
44	Evaluate the limit of \( \frac{\sqrt{x+1} - 1}{x} \) as \( x \) tends to infini…	Limits	View
45	Evaluate the limit of \( \frac{x}{x+3} + \frac{x-3}{x^2-9} \) as \( x \) tends …	Limits	View
46	Evaluate the limit of \( \frac{3 - x}{6} \) as \( x \) approaches 3.	Limits	View
47	Evaluate the limit of \( \frac{3x - 7}{2x - 1} \) as \( x \) approaches \( \fra…	Limits	View
48	Evaluate the limit of \( \frac{\sqrt{4+x} - 2}{x} \) as \( x \) tends to 0.	Limits	View
49	Evaluate the limit of \( \frac{e^{2-x} - 1}{x - 2} \) as \( x \) tends to 2.	Limits	View
50	Evaluate the limit of \( \frac{x^n - y^n}{x - y} \) as \( x \) approaches \( y …	Limits	View
51	Evaluate the limit of \( \frac{x + 1}{\sqrt{x^2 + 3x - 2}} \) as \( x \) tends …	Limits	View
52	Evaluate the limit of \( \frac{2x^2 - 3}{5x^2 - x} \) as \( x \) tends to infin…	Limits	View
53	Evaluate the limit of \( \frac{3x^2 + 3ax - 2a^2}{x^2 - a^2} \) as \( x \) tend…	Limits	View
54	Evaluate the limit of \( \frac{\sqrt{x} - 2}{x - 4} \) as \( x \) approaches 4.	Limits	View
55	Evaluate the limit of \( \frac{3x^4 + 6x}{x^2 + 4} \) as \( x \) tends to infin…	Limits	View
56	Evaluate the limit of \( \frac{2x}{\sqrt{x^2 + 1}} \) as \( x \) tends to infin…	Limits	View
57	Evaluate the limit of \( \frac{3 - \sqrt{x}}{9 - x} \) as \( x \) approaches 9.	Limits	View
58	Evaluate the limit of \( \frac{(x+3)(2x-1)}{x^2 + x - 2} \) as \( x \) approach…	Limits	View
59	Evaluate the limit of \( \frac{x^2 + \sqrt{x} + 2}{x^2 - 11} \) as \( x \) appr…	Limits	View
60	Evaluate the limit of \( \frac{\sqrt{x+1} + 1}{\sqrt{x+1} - 1} \) as \( x \) te…	Limits	View
61	Evaluate the limit of \( \frac{e^x + e^{-x}}{e^x - e^{-x}} \) as \( x \) tends …	Limits	View
62	What is the limit of \( \frac{e^{\cos x} + e^{\sin 2x}}{e^{\cos x} + e^{-\sin 2…	Limits	View
63	Evaluate the limit of \( \frac{\cos x - \sin 2x}{x^2} \) as \( x \) approaches …	Limits	View
64	Evaluate the limit of \( \frac{\ln(e^{3x} - 5x)}{x} \) as \( x \) approaches 0.	Limits	View
65	Evaluate the limit of \( \frac{\ln(\cos 3x)}{\ln(\cos 2x)} \) as \( x \) approa…	Limits	View
66	Evaluate the limit of \( \frac{e^{1/x} - e^{-1/x}}{e^{1/x} + e^{-1/x}} \) as \(…	Limits	View
67	Evaluate the limit of \( \frac{5 - \sqrt{x}}{x - 25} \) as \( x \) tends to 25.	Limits	View
68	Evaluate the limit of \( \frac{1}{x} - \frac{1}{\sin x} \) as \( x \) tends to …	Limits	View
69	Evaluate the limit of \( \frac{8^x - 2^x}{4x} \) as \( x \) tends to 0.	Limits	View
70	Evaluate the limit of \( \frac{\ln(2 + x)}{x + 1} \) as \( x \) tends to -1.	Limits	View
71	Evaluate the limit of \( \frac{e^x - 1}{\tan 2x} \) as \( x \) tends to 0.	Limits	View
72	Evaluate the limit of \( \frac{\cos x - 1}{\cos 2x - 1} \) as \( x \) tends to …	Limits	View
73	Evaluate the limit of \( \frac{\ln(\sec 2x)}{\ln(\sec x)} \) as \( x \) tends t…	Limits	View
74	Evaluate the limit of \( \frac{4}{x^2 - 4} - \frac{1}{x-2} \) as \( x \) tends …	Limits	View
75	Evaluate the limit of \( \frac{\cos 2x - \cos x}{\sin^2 x} \) as \( x \) tends …	Limits	View
76	What is the limit of \( \frac{x^2 - 4}{x - 2} \) as \( x \) approaches 2 using …	Limits	View
77	In Example 5, what was the final result of evaluating the limit as \( x \) tend…	Limits	View
78	What is the limit of \( \frac{3 \sin 5x}{x} \) as \( x \) approaches 0?	Limits	View
79	What is the value of \( \cos(180^\circ) \) used in trigonometric limit calculat…	Limits	View
80	What is the value of \( \sin(360^\circ) \) used in trigonometric limit calculat…	Limits	View
81	In Model Question 19, what is the derivative of the denominator \( x^3 - 3x + 2…	Limits	View
82	Evaluate the limit of \( \frac{x^3 - x^2 - x + 1}{x^3 - 2x^2 + x} \) as \( x \)…	Limits	View
83	What is the limit of \( k \) as \( x \) approaches \( a \), where \( k \) is an…	Limits	View
84	Evaluate the limit of \( \frac{x^2 - 1}{x - 1} \) as \( x \) approaches 1.	Limits	View
85	Evaluate the limit of \( \frac{x(x+1)}{2\sqrt{9x^4 + 1}} \) as \( x \) tends to…	Limits	View
86	What is the limit of \( [f(x)]^n \) as \( x \) approaches \( a \)?	Limits	View
87	Evaluate the limit of \( \frac{2x + 1}{x - \sin 2x} \) as \( x \) tends to 0.	Limits	View
88	What is the limit of \( \frac{1 + \sqrt{x+2}}{1 - \sqrt{x+2}} \) as \( x \) ten…	Limits	View
89	Evaluate the limit of \( \frac{x+3}{x+2} \) as \( x \) tends to infinity.	Limits	View
90	In the expression \( \frac{x^2-4}{x-2} \), what is the value at \( x=2 \) befor…	Limits	View
91	Evaluate the limit of \( \frac{\ln x}{x} \) as \( x \) tends to infinity.	Limits	View
92	What is the limit of \( e^{-x} \) as \( x \) tends to infinity?	Limits	View
93	Evaluate the limit of \( \frac{\sin 3x}{\sin 2x} \) as \( x \) approaches 0.	Limits	View
94	What is the limit of \( \frac{1}{x^2} \) as \( x \) tends to 0?	Limits	View
95	Evaluate the limit of \( \frac{x^2 - 9}{x + 3} \) as \( x \) tends to -3.	Limits	View
96	If \( f(x) = x^2 \), what is the limit of \( f(x) \) as \( x \) approaches -2?	Limits	View
97	What is the limit of \( \frac{\sqrt{x} - \sqrt{a}}{x - a} \) as \( x \) approac…	Limits	View
98	Evaluate the limit of \( \frac{2x + 5}{3x - 1} \) as \( x \) tends to infinity.	Limits	View
99	Evaluate the limit of \( \frac{\sin x}{\tan x} \) as \( x \) approaches 0.	Limits	View
100	What is the limit of \( x^3 \) as \( x \) tends to negative infinity?	Limits	View
101	Evaluate the limit of \( \frac{x^2 + 1}{x^2 - 1} \) as \( x \) tends to infinit…	Limits	View
102	What is the limit of \( \ln(1+x) \) as \( x \) tends to 0?	Limits	View
103	Evaluate the limit of \( \frac{e^x - e^{-x}}{2} \) as \( x \) tends to 0.	Limits	View
104	Evaluate the limit of \( \frac{1 - \cos x}{\sin x} \) as \( x \) tends to 0.	Limits	View
105	What is the limit of \( \frac{5x}{\sin 2x} \) as \( x \) tends to 0?	Limits	View