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This set of MCQs is based on the concepts and learning about limits and derivatives, which are extremely crucial concepts in mathematics whose application is not only limited to mathematics but are also present in other subjects like physics.
What is the value of \(\lim\limits_{y \rightarrow \pi/2}\frac{sin x}{x}\)?
What is the value of \(\lim\limits_{y \rightarrow 0}\frac{sin3y}{3y}\)?
What is the value of \(\lim\limits_{x \rightarrow 0}\frac{x^2sec x}{sin x}\)?
What is the value of \(\lim\limits_{x \rightarrow 0}\frac{x \,tanx}{cot\, x}\)?
What is the value of \(\lim\limits_{x \rightarrow \infty}\frac{x sin\frac{2}{x}}{2}\)?
The derivative of x2 cos x is,
2x sin x – x2 sin x
2x cos x – x2 sin x
2x sin x – x2 cos x
cosx – x2 sin x cos x
limx→0 | sin x|/x is equal to,
1
–1
0
does not exist
If f(x) = x sin x, then f′(π/2) is equal to,
0
1
–1
1/2
limx→0 (cosec x – cot x)/x is,
-1/2
1
1/2
1
If f(x) = x100 + x99 + … + x + 1, then f′(1) is equal to,
5050
5049
5051
50051
Limx→0 log(1 – x) is equals to,
0
1
1/2
None of these
The value of Limx→01 (1/x) × sin-1 {2x/(1 + x²), is
0
1
2
-2
Limx→0 {(ax – bx)/ x} is equal to,
log a
log b
log (a/b)
log (a×b)
Limx→0 {(ax – bx)/ x} is equal to,
log a
log b
log (a/b)
log (a×b)
The value of limy→0 {(x + y) × sec (x + y) – x × sec x}/y is,
x × tan x × sec x
x × tan x × sec x + x × sec x
tan x × sec x + sec x
x × tan x × sec x + sec x
The expansion of log(1 – x) is,
x – x²/2 + x³/3 – ……..
x + x²/2 + x³/3 + ……..
-x + x²/2 – x³/3 + ……..
-x – x²/2 – x³/3 – ……..
The expansion of log(1 – x) is,
x – x²/2 + x³/3 – ……..
x + x²/2 + x³/3 + ……..
-x + x²/2 – x³/3 + ……..
-x – x²/2 – x³/3 – ……..
