Question

lim x tends to 4 x^2-7x+12÷x^2-3x-4​

Answer 1

Answer:

1/5

Step-by-step explanation:

Since it is giving 0/0 form on substituting x with 4.

Use L'Hopital's Rule

Take derivatives of numerator and denominator

d/dx (4x^2 -7x +12)

and

d/dx (x^2 -3x -4)

Now we are left with

lim (x–>4) 2x-7/2x-3

Now put value of x in above equation

to give us the answer

1/5

Answer 2

Solution :

when we have substitute x = 2 then we get 0/0,

Now Simplifying the Given limit :

$\rm \:\underset{x \longrightarrow2}{lim} \: \frac{ {3x}^{2} - x - 10 }{ {x}^{2} - 4 } \\ \\ \rm \:\underset{x \longrightarrow2}{lim} \: \frac{3 {x}^{2} - 6x + 5x - 10}{ {x}^{2} - {2}^{2} } \\ \\ \rm \:\underset{x \longrightarrow2}{lim} \: \frac{3x(x - 2) + 5(x - 2)}{(x + 2)(x - 2)} \\ \\ \rm \:\underset{x \longrightarrow2}{lim} \: \frac{(3x + 5) \cancel{(x - 2)}}{(x + 2) \cancel{(x - 2)}} \\ \\ \rm \:\underset{x \longrightarrow2}{lim} \: \frac{3x + 5}{x + 2} \\ \\ \rm \: = \frac{3 \times 2 + 5}{2 + 2} \\ \\ \rm \: = \frac{6 + 5}{4} \\ \\ \rm \: = \frac{11}{4}$

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