S₁ (3x²³ - 2x^²) dx -2х) -1

Q: Differentiate r(t)=

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Q: The sum of two positive real numbers x and y is 12. Find an x and y among these such that the…

A: The sum of two positive real numbers x and y is 12.

Q: Let z=f(x,y) = 20x² - 25xy + 16y². Find the following using the formal definition of the partial…

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Q: Q14) [2x (1+x²) x-(1-x²) (1+x²) +CB)- 10 (1+x¹) (1+x²) (1+x²)" (1+x²)" 11 +00) +CD) 11 10 12 1.1…

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Q: 5. r(x, y) = ln (x + y)

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Q: enomena. f(t) is the height in centimetres of the sea above mean sea level in Cape Town due to the…

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Q: О к The area of the bounded region below is ec x2 C X²

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Q: TL 9. The region R = {(x, y): 0 ≤ x ≤ 2, -√√1-(x − 1)² ≤ y ≤ √1 - (x − 1)²} in the transformation x…

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Q: . Determine the area below f(x) = 8x - 2x² and above the x-axis.

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Q: Calculate the derivative. ƒ"(1), f(t) = 15t t+1

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Q: 2. 2 y² - 4y + 10 dy

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Q: Find the area under the curve 4x²-3x+6 between x = -2 and x=3

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Q: •S√6 3. 2 √6-x² dx

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Q: Which of the following is not an indeterminate form? * ∞-∞ O Option 1 0/0 O Option 2 1∞ 1/0

A: Topic = Limits Correct option = 4

Q: 80 80 (20) If the graph of the function f(x) is stretched vertically by a factor 2 and then…

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Q: X hat is the value of lima f(a)-aƒ(x)? r-a

A: Topic:- limits

Q: (B) Use Tabular integration f(t³-4t² to evaluate the following: - + 5t+ 32) sin(t)dt

A: We nee to evaluate ∫t3-4t2+5t+32 sin(t) dt

Q: Find the area of the surface obtained by rotating the curve Y = from x = 0 to x = 1 about the…

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Q: 4. f(x, y) = 5xy - 7x² - y² + 3x − 6y + 2 5. f(x, y) = (xy − 1)² 6. f(x, y) = (2x - 3y)³

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Q: 2. A thermometer is taken from an inside room to the outside ,where the air temperature is 5° F.…

A: It is required to find the initial temperature of the inside room using the given conditions…

Q: 7. fx√x - 1dx 8. 9. √ (2) √2² - 1 da dx 1 15. dx 5x + 1

A: 7. ∫ xx-1dx

Q: given m=6, n=1, and v=(-4,7), what is v(n-m)?

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Q: n. 3' 11. In each of the following, express the required series in summation notation.' (b) Find the…

A: Let's find taylor series of given  function  f(x) = sin(2x) at x = pi/6.

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Q: 4.yy 2xsinx

A: Solution of the given differentiatial equation is .

Q: I. Find the general solution of the following: 2x* 1. dx 2.d = xy 3. dy = (6e³x + 1)dx

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Q: 5. If A is (8, -7) and B is (5, 16), find a unit vector in the same direction as AB.

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Q: The Bradford family wants to establish an ongoing scholarship award at a college. Each year in June…

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Q: Given the number or numbers where the function is discontinuous. Is the discontinuity removable?…

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Q: The total revenue (in hundreds of dollars) from the sale of x spas and y solar heaters is…

A: Concept: Rxx, Ryy, Rxy, are the double partial derivative of x and y Maximum condition:…

Q: (B) Use Tabular integration f(t³-4t² to evaluate the following: - + 5t + 32) sin(t)dt

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Q: 1. f(x) da converges, then If f(x) ≤ g(x) for all z in [a, +∞o) and converges. g(x) dx also

A: Given

Q: Determine if there are any inflexions on the graph given by y=2x4-3x³+ x²+6. Proof they are points…

A: The given function y=2x4-3x3+x2+6

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A: topic- indefinite integral

Q: stion T1_Q3 rove by contradiction that there are no positive integers p and q such that 4p²-q² = 25

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Q: Part II. Calculating Second Order Partial Derivatives. Find all the second order partial derivatives…

A: Note : As per our guidelines we are supposed to answer only 3 subparts if there are multiple subpart…

Q: 7. y - 5y + 7y" - 5y' + 6y = x² + 3x - 5 Ans: y = C₁e³x + C₂e²x + C3 cos x + C₁ sin x + x² + ²x -…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: 3x · Se³ª sec e³ª tan e³ dx

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Q: Solve the given by simple substitution (2x + y)² dx - 2dy = 0

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Q: Determine the antiderivatives of the following functions: 4. f(3x² +1)4 x dx 5. s dx

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Q: Q1/Without using L'Hopital rule, find the following limit. +². lim

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Q: 3 S² 2 (3x+1) dx x-1

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Q: .2 3. If o (x) = f Ví dt, then 0 (a) 2x2 (c) O do dx (6) SA (d) 1. is

A: ϕx=∫0x2tdt

Q: -15 Evaluate the integral: -dz x²√²+64 (A) Which trig substitution is correct for this integral? 0x…

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Q: Find the nth Taylor polynomial for the function, centered at c. 1 f(x) n = 4, c = 2 +2² P4(x) = = =

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