The number of points in (-infty, infty),for w | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let $f(x) = x^2$ and $g(x) = x \sin x + \cos x$. We want to find the number of solutions to $f(x) = g(x)$.$f(0) = 0$ and $g(0) = 1$. Since $f(0) <

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(C) Let $f(x) = x^2$ and $g(x) = x \sin x + \cos x$. We want to find the number of solutions to $f(x) = g(x)$.$f(0) = 0$ and $g(0) = 1$. Since $f(0) $f'(x) = 2x$ and $g'(x) = x \cos x$.For $x > 0$,$f'(x) = 2x$ and $g'(x) = x \cos x$. Since $\cos x \le 1$,$g'(x) \le x  0$. Thus,$f(x)$ grows faster than $g(x)$ for $x > 0$.Since $f(0)  0$.Since both $f(x)$ and $g(x)$ are even functions,there is also exactly one intersection point for $x Therefore,there are exactly $2$ points of intersection.

The number of points in $(-\infty, \infty)$,for which $x^2-x \sin x-\cos x=0$,is

Similar Questions

The lengths of the sides of a triangle are $10+x^2$,$10+x^2$ and $20-2x^2$. If for $x=k$,the area of the triangle is maximum,then $3k^2$ is equal to

The maximum value of the function $f(x)=3x^3-18x^2+27x-40$ on the set $S=\{x \in R : x^2+30 \leq 11x\}$ is

The maximum area of the rectangle that can be inscribed in a circle of radius $r$ is:

If $y = a \log |x| + b x^2 + x$ has its extremum values at $x = -1$ and $x = 2$,then

The maximum value of ${\left( {\frac{1}{x}} \right)^x}$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module