Q.37 Find the values of a and b so that the function f given by f(x)=1 , if x≤3ax+b , if 3<x<57 , if x≥5 is continous at x=3 and x=5.

Q.37 Find the values of a and b so that the function f given by $f (x) = \{\begin{matrix} 1, i f x \leq 3 \\ a x + b, i f 3 < x < 5 \\ 7, i f x \geq 5 \end{matrix}$ is continous at x=3 and x=5.

$f (x) = \{\begin{matrix} \frac{\sin (a + 1) x + \sin x}{x}, f o r x < 0 \\ x, f o r x = 0 \\ \frac{\sqrt{x + b x^{2}} - \sqrt{x}}{b x^{\frac{3}{2}}}, f o r x > 0 \end{matrix}$

Put the parts in order to form a sentence. When you think your answer is correct, click on "Check" to check your answer. If you get stuck, click on "Hint" to find out the next correct part.

Q.37 Find the values of a and b so that the function f given by f(x)=1 , if x≤3ax+b , if 3<x<57 , if x≥5 is continous at x=3 and x=5.

f(x)=sina+1x+sinxx, for x<0x, for x=0x+bx2-xbx32, for x>0

Q.37 Find the values of a and b so that the function f given by $f (x) = \{\begin{matrix} 1, i f x \leq 3 \\ a x + b, i f 3 < x < 5 \\ 7, i f x \geq 5 \end{matrix}$ is continous at x=3 and x=5.

$f (x) = \{\begin{matrix} \frac{\sin (a + 1) x + \sin x}{x}, f o r x < 0 \\ x, f o r x = 0 \\ \frac{\sqrt{x + b x^{2}} - \sqrt{x}}{b x^{\frac{3}{2}}}, f o r x > 0 \end{matrix}$