Let a , b ∈ R , b ≠ 0, Define a function f(x)= begincasesa sin (π/2)(x-1), text for x ≤ 0 ( tan 2 x- sin 2 x/b x3), text for x0 endcases If f is continuous at x =0, then 10- ab is equal to

Question

Let a , b ∈ R , b ≠ 0, Define a function f(x)= begincasesa sin (π/2)(x-1), text for x ≤ 0 ( tan 2 x- sin 2 x/b x3), text for x>0 endcases If f is continuous at x =0, then 10- ab is equal to  (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

f(x)= begincasesa sin (π/2)(x-1), x ≤ 0 ( tan 2 x- sin 2 x/b x3), x>0 endcases For continuity at '0' displaystyle lim x arrow 0+ f ( x )= f (0) ⇒ displaystyle lim x arrow 0+ ( tan 2 x - sin 2 x / bx 3)=- a ⇒ displaystyle lim x arrow 0+ ((8 x 3/3)+(8 x 3/3 !)/ bx 3)=- a ⇒ 8((1/3)+(1/3 !))=- ab ⇒ 4=- ab ⇒ 10- ab =14

Q. Let a,b∈R,b=0, Define a function f(x)={asin2π​(x−1),bx3tan2x−sin2x​,​ for x≤0 for x>0​ If f is continuous at x=0, then 10−ab is equal to ____

f(x)={asin2π​(x−1),bx3tan2x−sin2x​,​x≤0x>0​ For continuity at '0' x→0+lim​f(x)=f(0) ⇒x→0+lim​bx3tan2x−sin2x​=−a ⇒x→0+lim​bx338x3​+3!8x3​​=−a ⇒8(31​+3!1​)=−ab ⇒4=−ab ⇒10−ab=14

Q. Let $a, b \in R, b \neq = 0$ , Define a function
$f (x) = {a sin \frac{π}{2} (x - 1), \frac{t a n 2 x - s i n 2 x}{b x ^{3}}, for x \leq 0 for x > 0$
If $f$ is continuous at $x = 0$ , then $10 - ab$ is equal to ____