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###### Jinesh Jain posted an Question
February 08, 2022 • 00:51 am 30 points
• IIT JAM
• Mathematics (MA)

# 42. let f:r >r be a wice differentiable 1+x ifx<0 44. 1f f (x) = (1-x)(px +g) f x20 satisfies function. if s(u,v)=s(u-then the assumptions of rolle's thcorem in

42. Let f:R >R be a wice differentiable 1+x ifx<0 44. 1f f (x) = (1-x)(px +g) f x20 satisfies function. If s(u,v)=s(u-then the assumptions of Rolle's thcorem in the interval-1,1], then the ordered pair (p.q) is du (a.) (2,-1) (a) 4(u-)r"u-v*) (b.) (-2,-1) (b.) 4u+)"u-v) (c.) (-2.1) (d.) (2,1) (C.) 2/ u-v)+4u-)s(u -v*) 45. Let f:RRbe a differentiable function (d) 2(u-v)s(u-v2) 43. Let A().S2(t).81 (). 82(t) be such that (2)=2 and )-sWs5(|x- |)° for all differentiable function on R. Let xe R. ye R. Let s(r) =rf(r). Then F()-() sa F(x)= Sa(he the determinant of &'(2)= i) Sa)| Then F'()is 81() 82 ()J (a.) 5 the matnx 15 (b.) equal to0 (c.) 12 (a.) S )81() S() 82()| |a "() 82()| (d.) 24 ) Sa ()A) 8r() (b.) 81(x) 8ax )82'() (ch() S'()_|A(x) 81()| 81)s2 (x)||S(x)82 () )S'() (d.) 81() () please provide us the solutions of all the sums, sir

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