Question

Решить lim (X стремится к 0)=cosx-5cosx/2x^2

Answer 1

Podstavliem znachenie x, ravnoe 0:
cos0-5cos0/2*0^2=1-5/0 = 1- "simvol beskonechnost' "= -beskonechnost'  (simvol - perevernutaia na bok vos'merka)

Answer 2

To solve the limit as x approaches 0 for the expression f(x) = (cos(x) - 5cos(x/2)) / x^2, we can simplify the expression and apply the limit. Here's the step-by-step solution:

Step 1: Simplify the expression: f(x) = (cos(x) - 5cos(x/2)) / x^2

Step 2: Apply the double angle formula for cosine: cos(2θ) = 2cos^2(θ) - 1

cos(x) - 5cos(x/2) = cos(x) - 5 * (2cos^2(x/4) - 1) = cos(x) - 10cos^2(x/4) + 5

Step 3: Rewrite the expression: f(x) = (cos(x) - 10cos^2(x/4) + 5) / x^2

Step 4: Apply the limit as x approaches 0: lim(x->0) f(x) = lim(x->0) [(cos(x) - 10cos^2(x/4) + 5) / x^2]

Now, we can evaluate this limit by direct substitution:

lim(x->0) [(cos(x) - 10cos^2(x/4) + 5) / x^2] = [(cos(0) - 10cos^2(0/4) + 5) / 0^2] = [(1 - 10cos^2(0) + 5) / 0^2] = [(1 - 10 + 5) / 0^2] = [-4 / 0^2] = [-4 / 0] = undefined

Therefore, the limit of f(x) as x approaches 0 is undefined.