The function $$f(x)=x2/a$$, $$0$$≤x

Question

The function $$f(x)=x2/a$$,    $$0$$≤x<$$1a$$,    $$1$$≤x<$$22b2$$−$$4b/x2$$,    $$2$$≤x<∞ Is continuous for $$0$$≤x<∞, then the most suitable values of a and b are

Infinity Learn · Accepted Answer

$$f(x)$$ is continuous at $$x=1$$.∴           $$f(1$$−$$0)$$ $$=$$ $$f(1)=f(1+0)$$⇒         $$1/a=a$$⇒$$a=$$±$$1$$.             $$f(x)$$ is continuous at $$x=2$$.∴          $$f2$$−$$0=f2=f2+0$$⇒       $$a=2b2$$−$$4b/2$$⇒$$b2$$−$$2b=2When$$  $$a=$$−$$1$$,$$b2$$−$$2b=$$−$$1$$⇒b−$$12=0$$⇒$$b=1$$.When  $$a=1$$,$$b2$$−$$2b=1$$⇒$$b=1$$±$$2Which$$ are not given.Hence $$(3)is$$ the correct answer.

$The function f (x) = \{\begin{cases} x^{2} / a, 0 \leq x < 1 \\ a, 1 \leq x < \sqrt{2} \\ (2 b^{2} - 4 b) / x^{2}, \sqrt{2} \leq x < \infty \end{cases}$ $Is continuous for 0 \leq x < \infty, then the most suitable values of a and b are$

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

The function f(x)=x2/a, 0≤x<1a, 1≤x<22b2−4b/x2, 2≤x<∞ Is continuous for 0≤x<∞, then the most suitable values of a and b are

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

$The function f (x) = \{\begin{cases} x^{2} / a, 0 \leq x < 1 \\ a, 1 \leq x < \sqrt{2} \\ (2 b^{2} - 4 b) / x^{2}, \sqrt{2} \leq x < \infty \end{cases}$ $Is continuous for 0 \leq x < \infty, then the most suitable values of a and b are$