Class-12-Math-Assignment-on-Continuity-Differentiation.pdf - Test-5 Time 1.5hrs Marks-15x5 Continuity Differentiation Q.1 Find the values of a and b

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CBSETODAY.COM Test-5 Time- 1.5hrs. Marks-15x5 Continuity & Differentiation Q.1. Find the values of a and b such that the function defined by f(x) = ( 5, if x 2 ax + b if 2<x<10 21, if x 10 ) is a continuous function Q.2. Find dx dy of sin 2 y + cos (xy) = π Q.3. Differentiate w.r.t. x (x cosx) x + (x sinx) 1/x Q.4. If x = t a 1 sin - , y = t a 1 cos - , show that x y dx dy - = Q.5. If y = (tan -1 x) 2 , show that (x 2 + 1) 2 y 2 + 2x (x 2 + 1) y 1 = 2. Q.6. Differentiate sin -1 + + x x 4 1 2 1 w.r.t. x Q.7. If x 0 1 1 = + + + x y y for -1<x<1, show that 2 ) 1 ( 1 x dx dy + - = Q.8. Find , dx dy if y = a t + 1/t , x = ( t + 1/t) a Q.9. Discuss the continuity of the function given by:- f(x) = x-1 + x-2 at x = 1, and x = 2.
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