If the two curves y=a^x and y=b^x intersect a | vedclass

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

Question

(A) Given curves are $y=a^x$ and $y=b^x$. At the point of intersection,$a^x = b^x$,which implies $x=0$. Thus,the curves intersect at the point $(0, 1)

Vedclass · Accepted Answer

$\frac{\log a-\log b}{1+\log a \log b}$

Vedclass · Answer

(A) Given curves are $y=a^x$ and $y=b^x$. At the point of intersection,$a^x = b^x$,which implies $x=0$. Thus,the curves intersect at the point $(0, 1)$. Let $m_1$ be the slope of the tangent to $y=a^x$ at $x=0$. $m_1 = \left. \frac{dy}{dx} ight|_{x=0} = \left. a^x \ln a ight|_{x=0} = \ln a$. Let $m_2$ be the slope of the tangent to $y=b^x$ at $x=0$. $m_2 = \left. \frac{dy}{dx} ight|_{x=0} = \left. b^x \ln b ight|_{x=0} = \ln b$. The angle $\alpha$ between the curves is given by $	an \alpha = \left| \frac{m_1 - m_2}{1 + m_1 m_2} ight|$. Substituting the values,we get $	an \alpha = \frac{\ln a - \ln b}{1 + \ln a \ln b}$.

If the two curves $y=a^x$ and $y=b^x$ intersect at an angle $\alpha$,then $\tan \alpha=$

Similar Questions

The differential coefficient of $f[\log (x)]$ with respect to $x$ when $f(x) = \log x$ is:

If $f(x)=3^x$ and $g(x)=4^x$,then $\frac{f^{\prime}(0)-g^{\prime}(0)}{1+f^{\prime}(0) g^{\prime}(0)}$ is

The derivative of $\log_8(\log_5 x)$ with respect to $x$ is:

If $y = \log_2(\log_2(x))$,then $\frac{dy}{dx}$ is equal to

Differentiate the following with respect to $x$: $\log (\log x)$,where $x > 1$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module