questions for practice

1.A

3.B

1 > Just exchange x with 1 / √ x , the equation would become -

c x ^{3 / 2} + b x ^{1 / 2} + a x ^{- 1 / 2} + 1 = 0

So the answer should be " D " .

6 > Observe that " a " must equal 1 , otherwise thre limit won't make any sense . After that , you just apply L - Hospital .

7 > The only critical point is zero . So check the continuity at x = 0 .

5)c ....(may be) coz θ'(x)=2f(x)f'(x)......nd f'(x) is +ve but f(x) can be negative or positive in [a,b]