Calculating $\lim\limits_{x \to 0} \frac{\sin^2(5x)-\sin^2(x)}{x \sin(7x)}$ [closed]

limits trigonometry

Solution 1:

$$\lim_{x \to 0} \dfrac{\sin^2(5x)-\sin^2(x)}{x \sin(7x)} = \lim_{x \to 0} \dfrac{25\left[\dfrac{\sin(5x)}{(5x)}\right]^2-\left[\dfrac{\sin(x)}{x}\right]^2}{7\dfrac{\sin(7x)}{7x}}$$

Could you complete now?

Related

Analytic solution to differential equations with reflected arguments
How to use Fermat's Little theorem in $12^{12^{12}}\mod{17}$? [duplicate]
Proving a language is not recognizable
Find a Möbius transformation such that a semi-circle in the upper half plane is mapped to $i\mathbb{R}_{>0}$
Is Haar measure reflection invariant?
$f(x+y)f(x-y)=[f(x)f(y)]^2$ implies $f(x)=g\left(x^2\right)$ for some $g$
Don't the derivatives of $\arctan x$ and $\operatorname{arccot} x$ imply they're negatives of each other?
How can i obtain general form of this integtral $\int_0^{\pi/4}\frac{x^3}{1+b\tan x}\ dx$
Proving a function on the discrete metric is continuous
Finding the value of the infinite product $\prod\limits_{n=1}^{\infty} \biggl(1-\frac{1}{2^{n}}\biggr)$ [duplicate]
Integral of Function in $L^p(E)$ Times Functions in Dense Set Being $0$ Implies Function is $0$
In most geometry courses, we learn that there's no such thing as "SSA Congruence".