Question

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Answer 1

Răspuns:

Calculezi  limita

L=x->1 lim[f(x)-f(1)]/(x-1)=

lim[√(8+x²)-√(8+1)]/(x-1)=

lim(√(8+x²-3)/(x-1)=Amplifici   fractia  cu(√(8+x²)+3=

lim[√(8+x²)-3][√(8+x²)+3]/(x-1)(√8+x²)+3)(x-1)=

lim[(8+x²-9)/(x-1)(√(8+x²)+3)=

lim(x²-1)/(x-1)(√(8+x²)+3]=

lim(x-1)(x+1)/(x-1)(√(8+x²)+3)=

lim(x+1)/(8+x²+3)=(1+1)/√(8+1)+3)=

2/(√9+3)=2/(3+3)=2/6=1/3

f `(x)=2x/2√(8+x²)=x/√(8+x²)

f `(1)=1/√(8+1)=1/√9=1/3

Explicație pas cu pas: