What is the limit as x approaches 0 of (7x^0e^{x^2})/(4x^2+2*0^2) ?

The limit as x approaches 0 of (7x^0e^{x^2})/(4x^2+2*0^2) is infinity

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limit as x approaches 0 of (7x^0e^{x^2})/(4x^2+2*0^2)

x \to 0 lim (\frac{7 x ^{0} e ^{x^{2}}}{4 x ^{2} + 2 \cdot 0 ^{2}})

\infty

Solution steps

x \to 0 lim (\frac{7 x ^{0} e ^{x^{2}}}{4 x ^{2} + 2 \cdot 0 ^{2}})

x \to a - lim f (x) = x \to a + lim f (x) = L

then

x \to a lim f (x) = L

x \to 0 - lim (\frac{7 x ^{0} e ^{x^{2}}}{4 x ^{2} + 2 \cdot 0 ^{2}}) = \infty

x \to 0 + lim (\frac{7 x ^{0} e ^{x^{2}}}{4 x ^{2} + 2 \cdot 0 ^{2}}) = \infty

= \infty

x \to 0 lim (x^{0} sin (\frac{1}{x}))

x \to 1 - lim (\frac{3}{1 - x})

x \to 0 lim (\frac{cos ( 20 x )}{x})

x \to 0 lim (1 - 2 x)

x \to 2 lim (2 x - 5)

What is the limit as x approaches 0 of (7x^0e^{x^2})/(4x^2+2*0^2) ?
The limit as x approaches 0 of (7x^0e^{x^2})/(4x^2+2*0^2) is infinity