What is the limit as x approaches 4 of arctan((x^2-16)/(7x^2-28x)) ?

The limit as x approaches 4 of arctan((x^2-16)/(7x^2-28x)) is arctan(2/7)

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limit as x approaches 4 of arctan((x^2-16)/(7x^2-28x))

x \to 4 lim (arctan (\frac{x ^{2} - 16}{7 x ^{2} - 28 x}))

arctan (\frac{2}{7})

Decimal

0.27829 \dots

Solution steps

x \to 4 lim (arctan (\frac{x ^{2} - 16}{7 x ^{2} - 28 x}))

\frac{x ^{2} - 16}{7 x ^{2} - 28 x} = \frac{x + 4}{7 x}

= x \to 4 lim (arctan (\frac{x + 4}{7 x}))

Plug in the value

x = 4

= arctan (\frac{4 + 4}{7 \cdot 4})

\frac{4 + 4}{7 \cdot 4} = \frac{2}{7}

= arctan (\frac{2}{7})

What is the limit as x approaches 4 of arctan((x^2-16)/(7x^2-28x)) ?
The limit as x approaches 4 of arctan((x^2-16)/(7x^2-28x)) is arctan(2/7)