P(C|AUB) P(AUB|C) = P(C|A) + P(C|B), where AnB = 0 = P(A|C') + P(B|C) − P(An B|C) P(Aº|B) = 1 − P(A|B)

Q: FX)=f(f(x))and G(x)= (F(x) F(4)=13f(13 )=3 f(13)=6f(4)=6 OF(4)- G'(4)=

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Q: エ+1 dx (7² +2x)

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Q: suppose

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Q: f:(-2,1]→[0,12] literal and overlapping function 12 if įs(x) dx = 13andſls*(x) đx =5 [f*(x) dx=? 10

A: Given :f:-2,1→0,12 literal and overlapping function.∫-21fxdx=13     →1∫06f-1xdx=5    →2To…

Q: S F(s) = (s + 5)(s² + 25).

A:

Q: (Inx)° dx = O 1) S(nx)* + С 2) (Inx) + C 3) (In x) + C 6x

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Q: For each statement, either prove that it is true or come up with a counter example N(ATA) = N(A) ● •…

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Q: P4: x3 (x² + 1)3

A: Use the algebraic substitution and solve the integration.

Q: 6. Evaluate: cin 4 a) (4x – 3) dx c) S* 2e* dx b) L, x²(-2x³ – 3)* dx d) ƒ dx e) S,(x + 1)(x² + 2x +…

A: (6) (a)To evaluate ∫254x-3dx Solution:…

Q: Let f(x, y) = e²x* %3D Evaluate f(3, 5)

A: Given :   f ( x, y) = exy x4   point ( 3,5)

Q: differe ntiato a) f(x) =10ge (X)x (3x)3 lincx))

A: Solution -  a.) Given function -  f(x)=log2(x) × (3x)3  We can write it as -…

Q: f(x, y) = x²/(1 + y²) (a) f(-5, 0) (b) f(14, 1) (-) (c) | (d) f(-8, y)

A: Put value of x and y in given equation.

Q: What is the point of intersection for f(x) = 2* and g(x) = A (1,) (0,1) C (1,0) (2,4)

A:

Q: f(x)= 1−x/ 1+x Evaluate:   a)  f(2)              b) f(−2)          c) f(a+1)

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Q: dx 7. JIVa² – 2x + 5 (hint: let æ² – 2x + 5 = (z – x)²) -

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

Q: find f c^) : 2x+3 5X+4

A: Topic :- Functions

Q: , if f (0) = 1 find f(1) s xf'(x)dx = 2x³ + 2x² + c O A) 5 O B) 15 OC) 10 OD) 7 O E) 8

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Q: Find f") if Aa) - (V 1)(x* - 1). %3D O a) -4 O b) 4 c) d) 1

A: Solve the following

Q: L L'FCE)]> F(4) = 4 sin #t

A: The solution is given as

Q: 2 (b) L1²}=3

A:

Q: The range of f(x)= 3+|x| is O (0,3] O (3,0) • 13, x) O (-x,3) 1Tx,3] (-x,3]

A: Explanation of the answer is as follows

Q: 2 Iƒ ƒn(x) = efn−1(x) for all ne N and fo If d nd {ƒn(x)}. dx

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Q: MacB = (x),ƒ o (1)fp хр = (x),f o %3D (x)fp = (x),f O %3D xp = (x),f o = sin x, which of the…

A: To find the correct option.

Q: S(x-ae )Vx² + 2e" dx -ах - ах 11.

A: Let's find.

Q: Let f(x)= x³+1. Then (fof)'(1)= O 20 O 36 O 3 O 9

A: Please refer to the image below

Q: 7. f f(x)= 4x+ 5, what is the value of f(-3)? 1) 17 2) -2 3) -7 4) 4

A: Answer (7)  Given ,  f(x) = 4x + 5  We have to find the value of f(-3)

Q: Find t for the following terminal points: (a) P(0, 1), t = (0) P(-, ), t =| (c) P(-1,0), t = (d)…

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Q: F(t) = A ₁² +B+³ 2 3 t

A:

Q: Proof [(pAq)=r] = [p=(q=r)] using the rule of replacement.

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Q: p(+) = + = Find P (Q(+) P(Q(r) Q (t)=1 ++1

A:

Q: 6) Let f f(x)dx 16, f(x)dx 10, fdx 5 then f(x)dx = A)-1 C) 31 B)-11

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Q: FG) ={(g6)) and 861)=2 Fing F'(2)

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Q: x -x-2 Find f"(3) if Ax)- x-2 O a) 1 O b) -1 O c) 2 d) -3

A: using quotient rule

Q: Determine n=0 1 L th (2n + 1)! An (x) An+1(x) dx, from the relation: n tn+1 LA -1 An (x) An+1(x) dx

A: Given Information:To find:The value of .Concept used:The power series of sine function is .