3.2 Inductive Reasoning Use inductive reasoning to make a conjecture. Note: The numbers 1, 2, 3, 4, 5, .. are called counting numbers or natural numbers. A. Consider the following procedure: 1. Pick any counting number. 2. Multiply the number by 6. 3. Add 8 to the product. 4. Divide the sum by 2. 5. Subtract 4 from the quotient. Solution: EXERCISE

Q: Use substitution to find the indefinite integral. 6 10(1

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Q: x’y? If z , show that x=+ y- 3z x+ y ôx ây a²z ô²z = 0 if z= Tan 2.xy x² – y? Show that âx² ' ây²

A: A detailed solution is given below.

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Q: of the indicated portion of the curve. K.

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Q: Q1: Define each of the following b) Normal group c) Nilpotent element d) Prime ideal e)Field.

A: Define each of the folowing:- b) normal group c) nilpotent element  d) prime ideal e) Field

Q: If y = 3 then dy/dx = 4+x O -6x/ (4 + x² )2 O 3x/ (4 + x² )² O 6x/ (4 + x² )2 O -31 (4 + x? )?

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Q: dy Find dt y = (21+ et) In t dy %D dt (Type an exact answer.)

A: To find the derivative of following function

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Q: 3. Solve the initial value problem of y(-1) = 0 dx x+3

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Q: V1. y=x' +1, the axes, x=3; 0X 1 y =-, , y-axis , y=1 & y =3 ; OY

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Q: 4 2. y =,x = 1,x = 4, and y = 0 is revolved about the y – axis. (Answer: 24n C. u. )

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A: Given ; Line meets plane = ?   x = -3 + 5t   y = 3 + 6t   z = -2 + 3t   Plane;        x + y + z =…

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A: Given

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Q: Find all angles, 0° < 0 < 360°, that satisfy the equation below, to the nearest 1oth of a degree. 4…

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Q: 11. (e* sin y – 3x²)dx + ( e* cos y+ |dy = 0 12. (2x + 1+x?y? ) dx +( -29) dy = 4 - 29) dy = 0…

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Q: 9. (2xy – sec?x)dx + (x² + 2y)dy = 0 10. (x + 3x³ sin y)dx + (x* cos y)dy = 0

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Q: Find (9x? - 8x + 2) dx. (9x² - 8x + 2) dx²

A: We know, ∫xndx= x(n+1)/(n+1) +C , C is a constant and for any real number n.

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Q: 3- Jッ 2X e dy + 2 (y ē -x) dx =0. dy よx 4- Sinx + cosx y = tan x

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Q: Evaluate dx 2 1-x

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Q: Use the tabular method to evaluate the integral fa (x³ + 2x-1) cos(4x)dx COS

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