Calculus IPU Fall
8 ay State Leibnitz theorem. If y= (c +V1l+x? y , Show that i, (14+x?)y, +29, —mPy =0 (4x? yg (20 Dag +07 m?)y, =0 b)/ State Rolle’s Theorem and wriie its geometrical meaning. Verify it for f(x) =…
78 ay State Leibnitz theorem. If y= (c +V1l+x? y , Show that i, (14+x?)y, +29, —mPy =0 (4x? yg (20 Dag +07 -m?)y, =0 b)/ State Rolle’s Theorem and wriie its geometrical meaning. Verify it for f(x) = (x —@)™(x — b)", xe[a, b] where m and n are positive integers. . CR
- b) Assuming the validity of the expansion, expand f(x) = tanx using Maclaurin’s series and hence the expansion of sec? x.
A worked answer is on its wayMeanwhile, read the Calculus I notes for this topic.
Discussion
Loading…
More Calculus I questions
a) Find the asymptotes of the curve: xtx?y—xy? y3+x? y? 2=0. b) i. Find the radius of curvature at any point of the curve 4+4 x =a(1+sint) y =a(a —cost) ii)…PU Spring7Attempt (Any three) of the following: 3x5 1 a) Evaluate: f dx b) Prove that = =2 —f ° Vx+Ja— x Saag © c) Evaluate: ¢ cos 30 sin? 60 d@ (apply beta gamma…PU Spring2a) State and prove Euler’s theorem on homogeneous functions of two : variables of degree n. If sinu= = then show that du du xx +y ra tanu. i i b) Find the…PU Spring19a) Find the maximum value of x? + y? +2? when +5 +7 = Lusing Lagrange’s multipliers method. b) Define Bernoulli’s equation. Solve: 2 +xsin2y =x° cos? y. OR…PU Spring8a) Find the general solution by using the method of variation of 2x parameters: y"—4y'+4y = x b) i. Solve the initial value problem: (x?D? — 3xD + 4)y = 0…PU Spring7Attempt all the questions 4x25 a) A function f(x) is defined as follows: 4= f= x, x<2 x 2, x22 p Show that f (x) is not differentiable at x = 2. (my b) Find…PU Spring2