If the angle between the curves y = a^x and y | vedclass

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

Question

(D) To find the intersection point,set $y = a^x$ and $y = b^x$ equal to each other:$a^x = b^x \implies (a/b)^x = 1 \implies x = 0$.For $x = 0$,$y = a^

Vedclass · Accepted Answer

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

Vedclass · Answer

(D) To find the intersection point,set $y = a^x$ and $y = b^x$ equal to each other:$a^x = b^x \implies (a/b)^x = 1 \implies x = 0$.For $x = 0$,$y = a^0 = 1$. Thus,the intersection point is $(0, 1)$.Now,find the slopes of the tangents at $(0, 1)$:For $y = a^x$,$\frac{dy}{dx} = a^x \ln a$. At $x = 0$,$m_1 = \ln a$.For $y = b^x$,$\frac{dy}{dx} = b^x \ln b$. At $x = 0$,$m_2 = \ln b$.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 of $m_1$ and $m_2$:$	an \alpha = \left| \frac{\ln a - \ln b}{1 + \ln a \ln b} ight|$.

If the angle between the curves $y = a^x$ and $y = b^x$ is $\alpha$,find the modulus of $\tan \alpha$.

Similar Questions

The derivative of $(\sin x)^x$ with respect to $x^{(\sin x)}$ is

If $y = \log_{10}x + \log_x 10 + \log_x x + \log_{10} 10$,then $\frac{dy}{dx} = $

$\frac{d}{dx}(5^{\log x}) = \dots$

If $y = e^{(1 + \log_e x)}$,then the value of $\frac{dy}{dx} = $

Let $f(x)=e^x$, $g(x)=\sin^{-1} x$ and $h(x)=f(g(x))$, then $\frac{h'(x)}{h(x)}$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module