The value of limx→∞x+cos xx+sin xis

Sail E0 Webinar

Question

The value of l i m x \to \infty \frac{x + c o s x}{x + s i n x} i s

Options:

A . -1

B . 0

C . 1

D . 2

Answer: Option C
:
C

l i m x \to \infty \frac{x + c o s x}{x + s i n x} [Putting x = \frac{1}{h}; a s x \to \infty, h \to 0] = l i m h \to 0 \frac{\frac{1}{h} + c o s (\frac{1}{h})}{\frac{1}{h} + s i n (\frac{1}{h})} = l i m h \to 0 \frac{1 + h c o s \frac{1}{h}}{1 + h c o s \frac{1}{h}} = \frac{1 + 0}{1 + 0} ⎡ ⎢⎢⎢ ⎣ \begin{matrix} ∵ - 1 \leq s i n \frac{1}{h} \leq 1 a n d - 1 \leq c o s \frac{1}{h} \leq 1, ∴ w h e r e h \to 0, h c o s \frac{1}{h} \to 0 a n d h s i n \frac{1}{h} \to 0 \end{matrix} ⎤ ⎥⎥⎥ ⎦ = 1

Was this answer helpful ?

Next Question

Submit Solution

More Questions on This Topic :

Question 1. If limx→0kx cosec x = limx→0x cosec kx , then k =....

Question 2. Limx→0tan−1x−sin−1xx3is equal to....

Question 3. Limx→0(1+x)13−(1−x)13x=....

Question 4. ABC is an isosceles triangle inscribed in a circle of radius r. If AB = AC and h is the altitude from A to BC.The triang....and A be the area of the triangle .Find limh→0AP3

Question 5. Let f be a function such that f(x+y)=f(x)+f(y) for all x and y and f(x)=(2x2+3x)g(x) for all x&#....g(x) is continuous and g(0)=9 then f'(0) is equals to

Question 6. The values of constants a and b so thatlimx→∞(x2+1x+1−ax−b)=12,are....

Question 7. If the derivative of the function f(x)=bx2+ax+4;x≥−1ax2+b;x<−1′, is everywhere conti....If the derivative of the function f(x)=bx2+ax+4;x≥−1ax2+b;x<−1′, is everywhere continuous, then

Question 8. Iflimx→−∞(√x2−x+1−ax−b)=0 then the values of a and b are given by....the values of a and b are given by -

Question 9. Limx→0(cosx)1/x4 ....

Question 10. If α is a repeated root of ax2+bx+c=0 then limx→αsin(ax2+bx+c)(x−α)2 is ....

Chapter 1 - GLOBAL STEEL SCENARIO & INDIAN STEEL INDUSTRY Part 1 : (13-04-2024) INDUSTRY AND COMPANY AWARENESS (ICA)

Direction Sense Test Part 1 Reasoning (Hindi)

Chapter 1 - RMHP / OHP / OB & BP Part 1 : (14-02-2024) GPOE

Cube & Cuboid Part 1 Reasoning (Hindi)

Data Interpretation (DI) Basic Concept Reasoning (Hindi)

Counting Figures Part 1 Counting Of Straight Lines Reasoning (Hindi)

Sail E0 free webinar Webinars

Real Numbers Part 7 Class 10 Maths

Real Numbers Part 1 Class 10 Maths

Polynomials Part 1 Class 10 Maths

Chapter 3.1 : INTRODUCTION Chapter 3 : Sinter Plant SAIL E0 - GPOE/GPA 2024

Chapter 2.3 : COAL HANDLING PLANT - Set 1 Chapter 2 : Coke Ovens and Coal Chemicals SAIL E0 - GPOE/GPA 2024

Chapter 1.1 : INTRODUCTION Chapter 1 : Raw Material Handling Plant SAIL E0 - GPOE/GPA 2024

GPOE / GPA Combined 1 Free Revision Test SAIL JO E-0

DSP Combined 1 Free Revision Test SAIL JO E-0