What is the limit as w approaches 0 of (a-sqrt(w^2+a^2))/(b-sqrt(w^2+b^2)) ?

The limit as w approaches 0 of (a-sqrt(w^2+a^2))/(b-sqrt(w^2+b^2)) is (a-sqrt(a^2))/(b-sqrt(b^2))

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limit as w approaches 0 of (a-sqrt(w^2+a^2))/(b-sqrt(w^2+b^2))

w \to 0 lim (\frac{a - w ^{2} + a ^{2}}{b - w ^{2} + b ^{2}})

\frac{a - a ^{2}}{b - b ^{2}}

Solution steps

w \to 0 lim (\frac{a - w ^{2} + a ^{2}}{b - w ^{2} + b ^{2}})

Plug in the value

w = 0

= \frac{a - 0 ^{2} + a ^{2}}{b - 0 ^{2} + b ^{2}}

Simplify

= \frac{a - a ^{2}}{b - b ^{2}}

t an g e n t 2 x^{2} + x - 3, at x = - 1

\int \frac{z}{1 - y ^{2} z ^{2}} d y

d er i v a t i v e y = \frac{x}{7} - \frac{7}{x}

x \to 0 lim (x ln (x) - x)

l a pl a ce t r an s f or m 3 + t^{5} + sin (π t)

What is the limit as w approaches 0 of (a-sqrt(w^2+a^2))/(b-sqrt(w^2+b^2)) ?
The limit as w approaches 0 of (a-sqrt(w^2+a^2))/(b-sqrt(w^2+b^2)) is (a-sqrt(a^2))/(b-sqrt(b^2))