Father of Calculus Isaac Newton and Gottfried Wilhelm Leibniz Hipparchus of Nicaea Antoine Lavoisier Gregor Mendel

Q: Suppose f(x, y) = xy² + 4. Compute the following values:

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Q: Use the theorem of Leibniz in the following problems: If y=x³e2x find y(m) and hence y(3). julm) =…

A: Leibniz rule states that (f(x)⋅g(x))n=∑r=0n Cr nf(n−r)(x)⋅gr(x) Let fx=e2x and gx=x3

Q: f(X) ex finathe cn'nical numbers of f O de remine whethereacn is a1ocaimaximum, 1ocalminiumum…

A: Critical points

Q: 1. How to solve the values of x to find the critical values of the graph of a polynomial function?…

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Q: find Ahe Longth o fthe cerc 2 froom @aobo @-

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Q: dx cot 2x cos 2x 4,

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Q: Approximate sin 49º by Taylor series

A: We know that,  49°  = 45° + 4°  = (π/4 + π/45) rad = (45+4)*π/180 =  49π/180 rad

Q: Find the distance traveled after 6 seconds by a particle whose velocity is v(t) = (t − 2) meters at…

A: Given

Q: 8. If y = (x* +2x²)e2* determine an expansion for y(5). %3D [y(5) = e2x24(2x³ + 19x² + 50x + 35)]

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Q: Find the work done by winding 3 meters of a cable if the force applied to wind the cable by x meters…

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Q: MULTIPLE CHOICE Question 5 Given the following matrices, find 2B- A. -20 5 3 2 0 and B = 17-3 4-3 1

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Q: 2. Let R be the region in the first quadrant bounded by the graph of y = Vx-2 and the lines x-2 and…

A: Note:  As per our guidelines, we are restricted to solve only one problem. Hope you will understand.…

Q: steel

A: Please refer to the image below

Q: (メ+ッ)dx + (x4ッ)dy =。 d x dy x yz x?y

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Q: A company produces a special new type of TV. The company has fixed costs of $486,000, and it costs…

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Q: (ax-2) dx x2+ 2X + 15

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Q: Confirm that the Integral Test can be applied to the series. Then use the Integral Test to determine…

A: Option (B) Diverges

Q: SET-UP ONLY the definite integral that will give the area of the region bounded by y = x +1 and x =…

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Q: Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in…

A: The height(cm) of the candle is a linear function of the amount of time (in hours) it has been…

Q: 4. csc 2x cx

A: The integration of the integral is csc52x.

Q: 2. Find the equation of the normal line to the graph of y = x²(1+ In.x) at x = e. Write your answer…

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Q: Using Wallis formula, find the integral of the expression. Answer in fraction form, no units, no…

A: Follow the procedure given below.

Q: Find all the second order partial derivatives of g(x.y) =xy +5 sin (y) + 4y cos (x). please solve

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Q: V. Determine all the relative minimum and maximum values, and saddle points of the function h…

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Q: Use the theorem of Leibniz in the following problems: 1. Obtain the n'th derivative of: x2y [x?y") +…

A: The objective of the question is determine the nth derivative of the given equation.

Q: 16-17. Find the derivative: y = (x2 – 4x + 2)(2x3 – x2 + 4) A) 2x*- 36x³ + 24x2 + 4x -1 B) 2x* –…

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Q: 3. Accumulate P2,500 at 5-% simple interest from November 6, 1988 to April 11, 1989. 12

A: Given :Principal = P2500Rate =535=285%Time : Nov 6, 1988 to April 11, 1989

Q: Newton's Law of Cooling says that the temperature of a cooling substance is T = A + (T, – A)e*t, A…

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Q: 6 4 Verify that for f(x, y) = 3x°y* - 4x°y°. дх ду ду дх of

A: Given problem:-

Q: Using Wallis formula, find the integral of the expression. Answer in 5 decimal places (example…

A: We have to solve given integration with the help of wallis formula.

Q: х3-4х-10 х2-х-6 (2x + 21n|x – 31 – 4 In |x + 2|) + C (2x + 2 In|x – 3| + 4 In |x + 21) + C Option 1…

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Q: Find f, fy. f- 2 f(x.y,z) = 3x - V4y +z" | (Type an exact answer, using radicals as needed.)

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Q: Evaluate the following indefinite integral: 2(1 + e*) dx (x + e*)3

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Q: The matrix is defined as A= 1 has characteristic equation of 22 + DA + 3, so the value of D…

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Q: find the Langth of the are Ve Siesinzo from to o-52

A: Given:        r=1+sin2θ   Interval is 0,2π  Length of the arc of the curve is given by…

Q: Example 2: Find the Fourier series 1, - 1<x < 0 f(x) = { 1," 0 <x < 1

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Q: :- 2)³. (2x + 1)* if y= 2x. 3x+8 dy Use logarithmic differentiation. Find dx

A: We know that power rule of derivatives is given as - d(xn)/dx = nxn-1.     Here i attached the…

Q: 26 The sum of two numbers is 40. Find the product of the numbers if their product is to be the…

A: As per the guidelines I am supposed to do the first question among multiple questions. To get the…

Q: (D4 – 2D3 + 5D² – 8D + 4)y = 0 (D3 – D² + D – 1)y = 0 (4D3 + 12D2 + 13D + 10)y = 0 (D5 + D4 – 7D3 –…

A: Given

Q: (y®+ 4y³-Ay) dy y2+10 6. ,3.

A: LetI=∫y5+4y3-4yy2+10dyI=∫y5y2+10+4y3y2+10+-4yy2+10dyI=∫y5y2+10dy+∫4y3y2+10dy-∫4yy2+10dyTake constant…

Q: It is estimated that x months from now, the population of a certain town will be changing at a rate…

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Q: 5. Find an expression for y(4) if y = e'sin t.

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Q: Identify the type of quadric surface defined by the equation 6x² + 3y² + 2z² = 36, and find all x-,…

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Q: polar com 2) (3, 240°) 90° 120° 60° 150° 30° 0- 180° 2 3. 330° 210° 300° 240° 270°

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Q: .In a particular very small region, the consumer price index, C, depends on the current value of…

A: Given information C=100+(e-EP)/Fwhere, C = Consumer Price Index E = Gross Domestic Regional…

Q: 3. X sinx eas x dx 2.

A: To find out the integration.

Q: In solving Optimization Problems, it is important to substitute zero to the 니o parameter being…

A: Here is the solution

Q: V2t-3-3 Find: lim t→6+ t-6

A: Given that we need to find the value of  following limit.

Q: Let f be the R 2 − R function defined by f (x, y) = ln xy and let r be the R − R 2 function defined…

A: Given

Q: 1. Let z = 3+ 6i and w = a + bi where a, b e R. Without using a calculator, (a) determine , and…

A: Let's find ratio of given complex numbers.