Find the limit: 1 / SiNx squared - 1 / X squared

Find the limit: 1 / SiNx squared - 1 / X squared

1/(sinx)^2 - 1/x^2 = [x^2 - (sinx)^2]/[xsinx]^2= [x^2 - (sinx)^2]/x^4*x^2/[sinx]^2lim_ {x->0}[1/(sinx)^2 - 1/x^2]= lim_ {x->0}[x^2 - (sinx)^2]/x^4*x^2/[sinx]^2= lim_ {x->0}[x^2 - (sinx)^2]/x^4= lim_ {x->0...

Subtract one square of SiNx from one square of X to find the limit X tends to 0

Limit 1 / x ^ 2 - 1 / SiNx ^ 2
=(sinx^2 -x^2)/ x^2*sinx^2
=(SiNx ^ 2 - x ^ 2) / x ^ 4 SiNx ^ 2 is equivalent to x ^ 2. Since the numerator denominator region is infinitely small, the derivative of the numerator denominator can be obtained
=(sin2x-2x) / 4x ^ 3 because the numerator denominator region is infinitely small, the derivative of the numerator denominator can be obtained
=2cos2x-2 / 12x ^ 2 because the numerator denominator region is infinitely small, the derivative of the numerator denominator can be obtained
=-4sin2x /24x
=-Sin2x / 6x sin2x equivalent 2x
=-2x/6x
=-1/3
When you use the theorem to judge, you must first check whether the condition of the theorem is applicable, that is, infinity / infinity, poor small / infinitesimal, otherwise you cannot use this theorem to derive up and down

Differential of y = cosx / (1 + SiNx)

y = cosx/(1+sinx)dy/dx = [(1+sinx)(-sinx)-(cosx)(cosx)]/(1+sinx) ²= (-sinx-sin ² x-cos ² x)/(1+sinx) ²= [-sinx-(sin ² x+cos ² x)]/(1+sinx) ²= - (sinx+1)/(1+sinx) ²= - 1/(1+si...

What is the number of real roots of equation 2 to the power of X - x = 3? Try to write the process, or write the real root. Ash is often anxious

From the images of F (x) = 2 ^ X and f (x) = x + 3, they have two intersections
So the number of real roots of the equation is 2

What are the number of real roots of equation (1 / 2) to the power of x = to the power of 1 / 2 of X

Anyway, 1 / 2 is one of the answers

It is proved that the equation E has at least one positive root less than 1 to the power of x = 3x

e^x=3x
f(x)=e^x-3x
Let x = 0
f(0)=e^0-0=1>0
Let x = 1
f(1)=e-3<0
Because f (0) * f (1) < 0
So there is 0, that is, e ^ x = 3x has at least one positive root less than 1