864.

lim⁡x→0(sin⁡6x4x+x2−xx)\lim_{{x} \to {0}}\big(\frac{\sin6x}{4x}+\frac{x^2-x}x\big)

TEKST ZADATKA

Odrediti graničnu vrednost:

lim⁡x→0(sin⁡6x4x+x2−xx)\lim_{{x} \to {0}}\bigg(\frac{\sin6x}{4x}+\frac{x^2-x}x\bigg)
REŠENJE ZADATKA

Raščlaniti izraz.

lim⁡x→0sin⁡6x4x+lim⁡x→0x2−xx\lim_{{x} \to {0}}\frac{\sin6x}{4x}+\lim_{{x} \to {0}}\frac{x^2-x}x

Pomnožiti prvi razlomak sa 66.\frac 66.

lim⁡x→0sin⁡6x4x⋅66+lim⁡x→0x(x−1)xlim⁡x→0sin⁡6x6x⋅64+lim⁡x→0(x−1)\lim_{{x} \to {0}}\frac{\sin6x}{4x}\cdot\frac66+\lim_{{x} \to {0}}\frac{x(x-1)}x \\ \lim_{{x} \to {0}}\frac{\sin6x}{6x}\cdot\frac64+\lim_{{x} \to {0}}(x-1)

Primeniti tablični limes: lim⁡x→0sin⁡xx=1 \lim_{{x} \to {0}}\frac {\sin{x}} {x}=1

1⋅32+lim⁡x→0(x−1)1\cdot\frac32+\lim_{{x} \to {0}}(x-1)

Zameniti x=0.x=0.

32+0−112\frac32+0-1 \\ \frac12