1. cosh (j) 2. tanh 3. 3. In(2 + j3)

Q: x+y uis = 1 n upi = no • prove that x-+ y-

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Q: - Evaluate Lf²f²8x³yz dr dz dy.

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Q: if x~unif. (0,2),find the U.b. of p(lx - mul>= 2)

A: Given X~Unif(0,2) Result: if X~unif(a,b) then  Mean=(a+b)/2 Variance=(b-a)2/12

Q: suppose

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Q: Using an appropriate substitution, i) Evaluate [x (1- x)³ dr.

A: The solution for the above question is as shown below.

Q: If lal = n, show that |a'| %3D gcd(n,t)

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Q: ไ1,) จงพิจารณาว่าอินทิกรัลไม่ตรงแบบต่อไปนี้ลู่เข้าหรือลู่ออก 1. dx 5. (๕๔) ห 7. dx

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Q: Prove That:- o sinhz= loy (Z+lz*+l )

A: To prove, sinh-1z=logz+z2+1     Lets consider, y=sinh-1z…

Q: If h(X) =n) 3+3F(X) where FC1) =7 and f'(1) what is h'LI) ?

A: If h(x) = 3+3f(x)   where f(1) = 7 , f'(1) = 2 differentiate h(x) with respect to x.   then put x=1

Q: 9. Prove L'S 25+1 Cs+2)?(S-1)2. %3D

A: Consider F(s) = 2s+1(s+2)2(s-1)2                            (1) Let 2s+1(s+2)2(s-1)2 =…

Q: 7. (a) cosh?1 (b) 2 sinh² 20

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Q: 2 4 Differentiate cxprersion (use D for dy X y' w. respect tox

A: on diffrentiating with respect to x we get

Q: If y- sinhx then prove that = dx

A: Fundamental inverse Trigonometric Identities: →cosh2y - sinh2y = 1 Basic derivative:…

Q: Find an expression for f (t, p) and evaluate that expression when t = 0. Find an expression for f(t,…

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Q: 15. Let fx)- Find tuntions +3 %3D Flalx) = get (x) =

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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 7(t) = VE + 4, cos(t), te-'> (t*), te¯t >

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Q: 20) S(tanh (4– 3x) kdx

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Q: Q3. Find y= fx) such that y

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Q: 10) [2* dx

A: given,         ∫2-4xdx

Q: Ql if (x,y,z) =o and Z"=x+Y find d2 (using di f Beren tials concept)

A: Given  If f(x,y,z) = 0 and z2 = x + y

Q: 7. S X e dx - X et + 4e¯x

A: As we know from the exponent rule: xaxb=xa-b And the common integral is: ∫1ax+bdx=1alnax+b+C   The…

Q: +9y-2x+4X +7 3X -2X =D3e te

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Q: 4. If /(r.y)=- , find f, and f,. V+y

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Q: Find dy Ser ysX"+3*+ e° dx + sin (1nx)

A: Given that: y=xy+3x+ecos-1x+sinlnx

Q: 4. Find f"(2). (a) f(u) = 2u²5 – u).

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Q: obtan al the real solutons af 4sinhte 4onh 42 -17 sinh3x + 4 sinhzz =0

A: Note that x=0 is a solution of 4sinh4x-17sinh3x+4sinh2x=0.

Q: ) FIND F'6): c. f() - x 2- 3x2 F. f6) = VI-x

A: f(x)=x2-3x2differentiate w.r.t.…

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

A: Solve the following

Q: 11. V =tr²h (h) constant as A) ans :V' (h) = tr²h 3.

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Q: cancer u alcurate 5th on diagnostic test is 9s 2 those who halse A 'cancer cnd on those wno do not

A: Given that, As the test is 95% accurate for both who have cancer and who don’t, therefore the…

Q: 10 6. Evaluate -dx. (x – 1)(x² + 9)*

A: Given integral is We will evaluate the integral by using the concept of partial fraction…

Q: Đi bỏ xes xdx = dx 2) √ √9+4x² = a) 6e5-1 25 ¹ (²3) + a) cosh-1 c b) 1+4e5 25 b) (4e5-1) 25 c). sinh…

A: Using following formulas

Q: =/4 sin z 23)/" dr cosr

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: If P(A or B) = 0.801, P(B') = 0.33 and P(A and B) = 0.20. Find i) P(B) ii) P(A)

A: Answer: Given that, P(A or B) = 0.801 P(B') = 0.33 P(A and B) = 0.20