Section 1: Real Numbers Note, Paccign. 1. Rationalise and fully simplify the denominator of the following surd: 2+√7 2-a√7

Q: Solve the following IVP: * = 1² * [1 2 13 2 x(0) = = [4]

A: NOTE: Refresh your page if you can't see any equations. .

Q: Find the solution to the differential equations xdt = (t³ — 3t) In² xdx

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Q: Evaluate the definite integral. -3 [₁₁2+. -3 (x+3) ex²+6x+8 dx =

A: ∫exdx=ex+c∫xndx=xn+1n+1+c

Q: Find the integral of the following function by parts ² axebx dx where a = 1.9, b = 0.1 in radians…

A: NOTE: Refresh your page if you can't see any equations. . here we have a=1.9 and b=0.1

Q: sto viloloy sif Ea 3 ²³ (1 +6w² - 10w²) dw

A: I have appended the formula used in the solution part of the question

Q: Using Green's Theorem, compute the counterclockwise circulation of F around the closed curve C. F =…

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Q: (1) Let y = Σnz". (a) Compute y' and write out the first four terms of the series. (b) Compute y"…

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Q: Determine the singular points of the given differential equation. Classify each singular point as…

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Q: Consider the region bounded by the lines y = √, y = 0, and x = 4. Suppose this region is rotated…

A: According to question,Given Curve,y = x,y=0andx = 4Axis of raotaion through x=-1

Q: a.y=k√√x-z² k√√x b.y=2² c. y = k₁√/xz² d. y = k + √√xz² represent

A: we will find the required.

Q: Evaluate the indefinite integral. Integral = + C [ 2³ (2² + 3)¹/² dz

A: We will use substitution method to solve this integral.

Q: Solve the initial value problem. y"+6y' +9y=0, y(0)=2, y'(0) = -5

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Q: Question 9 Solve the differential equation. y'e³x + 3ye³x = 4x A) y = 4x²e3x + ce³x B) y = 4x²e-3x +…

A: Topic = Differential Equation Correct Option = C

Q: Setup the Riemann sum 5 n [²³x³ dx = lim Σ n→∞ k=1 b f(x) dx n = lim Σ f(x)Ax for the given…

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Q: 1. The equation x² + y² = 1 defines the unit circle with its centre at the origin. The circle passes…

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Q: Given the demand equation x = 120e-P/26, where p represents the price in dollars and a the number of…

A: elasticity of demand  E(p)=px*dxdp.......(1)

Q: Find the Maclaurin series for the function. (Use the table of power series for elementary…

A: NOTE: Refresh your page if you can't see any equations. . the given function is

Q: Evaluate the definite integral. ₁42² +4 dz= x²

A: NOTE: Refresh your page if you can't see any equations. .

Q: Find the distance between the points (63, 89) and (72, 49) Distance =

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Q: 3-t Let F(x) = √² + 40 (a) Find the value of a where F obtains its maximum value. x = dt for -∞0 < x…

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Q: This problem will lead you through the steps to answer this question: A spherical balloon is being…

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Q: Prove or disprove that f(x,y): = x² - y² x² + y² is continuous at the origin.

A: Topic: Limit and Continuity   The answer is given in step 2

Q: Solve the system of linear equations. (If the system is 3y + 5z -16 y 2z = -50 y + z = 7 2x 4x -X-

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Q: g(1) = g(2) = g(3) = g(6) = B. On what open interval(s) is g increasing? C. At what value of x on…

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Q: on by parts to evaluate the indefinite integral S 2x sin(x) dx.

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Q: A retailer needs to purchase 12 printers. The first printer costs $54, and each additional printer…

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Q: Write an expression that gives the requested term. The 11th term of the geometric sequence with…

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Q: When an object is dropped on a certain earth-like planet, the distance it falls in t​ seconds,…

A: Motion: Recall that the velocity is the time derivative of the position, and the acceleration is the…

Q: Compute the definite integral fre™ dr.

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Q: Find the area of the region. y = 16 - x4 15 10

A: Area of the shaded region Area ( A ) = ∫x1x2ydxGiven y = 16 - x4

Q: Use the substitution x = 5 sint to evaluate the integral f√25 – x² dx.

A: ∫ cos(at) dt = 1asin(at) +C.

Q: Let f(x) = (In x)² f'(x) f'(e¹) = |

A: dxndx=nxn-1d dx(lnx=1xlne=1given  f(x)=(lnx)7 f'(x)=d dx(lnx)7

Q: Find the indefinite integral. (Use C for the constant of integration.) Ï 11 (z - 12) ¹1 dz

A: Use the substitution method to find the indefinite integral.

Q: Answer: 3 = f*f(x) dx = f(x) dx = 50, find If f is continuous and ³ ['ƒœ f(3x) dx.

A: I am attaching image so that you understand each and every step.

Q: Evaluate the integral - dz 2./or using trigonometric substitution.

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Q: - 8x² Find the critical points of the punction y=x4.

A: Topic - Critical points of the function We are given y=x4-8x2critical points of function are found…

Q: The population of a herd of deer is represented by the function A (t) = 195(1.31)t, where t is given…

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Q: 1. y = C₁ cos wt + C2 sin wt; w a parameter not to be eliminated.

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Q: Select all limits for which L'Hopital's Rule can be applied. Tim X→ 1+ (x ex 1)(x - 2) 3In(x) lim x+…

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Q: Find the length of the loop of the given curve. x = 9t-3t³ y = 9t² 6 5 e +39 X

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Q: 3. Given: sin(0) = cos(p) = Show all work! Find: sin(0 + p) π where = < 0 < π 2 5 where π < φ< 13 3π

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Q: 1) [20 pts] Find the gradient of f(x,y,z) = e* (sinxz) (lnyz) at the point (1,2,3)..express…

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Q: Find dy/dx for y= square root of u and u=x2+6.

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Q: Q7. Please answer all the parts to this question

A: To find out the derivative dF/dr.

Q: Using Formula 1, find the arclength of a semicircle given by x = cost, y = sint, t = [0, π].

A: Given curve:- x=cost,y=sint, t∈0,π

Q: 2. Given the vectors and u = (3,−4), v = (−1,2) find |2u + v, |2u|+|v|| Answer: √61,10 + √5

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Q: Use the principle of mathematical induction to show that the statement is true for all natural…

A: Use the basic principle of mathematical induction to prove this statement.

Q: The midpoint of AB is at (-4,-2). If A = (4, 6), find B. B is:(

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Q: deposited at the end of each quarter in an account that earns 5% compounded quarterly until $70,000…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Given the geometric sequence 3 ان دا دات 3,125 625 125 48 24 96 www** what is a6?

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