Theorem 17 F zO Hhen sF=0 If and only If f=o Q.e IF SF= fF AIB Proof: (E If F=O Qe then %3D A1B MCB) = 三の (->) suppose S F=0 Tet An= XEA ; F(2) >I Note FZ! AAniA %3D So 0= X. Am iA 8o Hin M(An)= But B= $ }= N An XEA: F(2) >o %3D 30 30 F= 0 Question a Hhe Can the assumption f zo kheorem 17?- be dropped in

Q: Solve the following ODEs by making an appropriate change of variable: (a) (y² − z²) dy = –2xy, 1-3y…

A: I have explained everything within the solution .please go through that.

Q: の x?. xy- yーx find %3D of 3 f Fex)こ X²+5x+2 Find f cl Q Let texl= goe) Find fezt ifgeziz=3_ find…

A: Differentiating the functions

Q: Differentiate y = VIn x 2 Inx +1 A. 2(In x)2 3. Inx-1 3 (In x)2 2 Inx-1 C. 2(In x)2 13 1. D. 3) 2(In…

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Q: Find if y = tan- 5). Select one: A. 1-) В. 1+ (1 – 2)* C.d - 2 O D. I+ (1 - 1)* OE.+ (1-)

A: Given function is We know that derivative of tan inverse x is 1/1+x^2,so

Q: re 1 da Ji rVI- (In x)²

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Q: | sec(/I) tan(/) dr

A: We need to solve integral.

Q: Suppose that I'm (f`∞x) = (x (24-1) and f(0) = 3-2i, f(1) = 6 -21, Find f(1+i)

A: Given that Imf'z=6x2y-1 To find: f(1+i).

Q: Hw) if J-0- Gso and X=O+ Cas e Show that Sece+tan 0

A: The given differentiation can be solved by using chain rule. Initially, the y expression can be…

Q: 96, a0ose -bsine =0 a'simo +baose asimo-baose Then,

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Q: b) f′(6)≈ c) f′(4)≈

A: To find out the slopes by the help of table.

Q: y=ー-x+5 3 y=-x+7

A: This question is based on Substitution.

Q: Show that is Reciz) e -ImZ p (ii) Im(iz) = Relz). %3D

A: Solution:- we have to show that  (1)    Re(iZ) = - ImZ (2)    Im(iZ) = Re(Z) where , Z = x + iy

Q: Q1: if AB = i+ 4j – 2k and B is the point (5,1,3), find point A.

A: AB vector is given. AB = i +4j -2k   Creat vector AB by taking variable point A and given point B…

Q: Evaluate [²√₁-Pa dx °ex√1_(ex)2 ofile कस 0 √i-(ex)

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Q: Find sin a. (-/5 ,2) [ ?] 1

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Q: A particular solution of y" + y =sinx + xcosx a. x?sinx - 2xcosx) 4 b. (x?sinx – xcosx) 4 c. (x?sinx…

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Q: 1. dy = %3D COSX cotytanx Cosy dr

A: Given- dy=1cotytanx-cosxcosydx To solve the given differential equation. Here we will arrange the…

Q: 1) Ans. in 2 frvr* +9dx Ans. 98/3 2)

A: Consider the provided expression, ∫2233dxx-x13 Solve the provided integral. Apply the u substitution…

Q: P(A)=0.3, P(B)=0.6, A and B are indep, find P(AB'), P(A|B')

A: We have given that  P(A) = 0.3 P(B) = 0.6 If A and B are independent then, P(AB) = P(A and B) =…

Q: L (e*** sin 4t). 4e 4e s +16 (s+3) +16 O A.) B.) 4e 4e (s - 3)' +16 (s - 3)(s +16) O C) O D.)

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Q: (c) = y² %3D dr dy (d) y = sin x %3D

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Q: differen tiatin, de tomine dx リ= (aH) (xs) 5 (as) (x-+)

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: iv) z1 = et01 ,zZ2 = el®2 then z,.Z, = ei(8,-02).

A: Here, the given statement is wrong.