3. Tunctio T(X), WhOSe graph is shown below. Determine the limit of a function, by observing the behaviour of the graph.

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A: Given question:- C.) What is the limit of function.

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A: The given limit problem is solved below.

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A: This question is related to behavior of infinite series, we will solve it using Ratio Test. 

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A: 4 Find the directional derivative of f (x,y)= 2x^2 y^2 -3xy at the point (1,-1) in the direction a. ...

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Q: -5x + cos (9x) – 1 Evaluate lim 2x Submit an exact answer.

A: To Evaluatelimx→0-5x+cos(9x)-12x  

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Q: Convert the polar coordinates below to Cartesian coordinates. Give exact answers. A. If (r, 0) = (5,...

A: Cartesian coordinates of the above polar coordinates are

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A: To find the general solution of the differential equationdydx=- 2x2+y22xy+3y2

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Q: 1. Evaluate the following limits. 3x + 10 – 4 (a) lim 2--2- r2 – 4x + 4

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Q: EVALUATE INTERMS OF GAMMA FUNCTION.

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Q: Evaluate the integral f 2x (x² + 5) dx using the substitution 13 u = x +5. 2x (x² + 5)*° d =| +C

A: I =∫ 2 x (x2+5)13 dx  u = x2+5du = 2x dxI =∫ u13  du We know that,∫ xn  dx =xn+1n+1+C

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Q: 2. Let b 1, and graph C ate- using different values for a. Explain the effect of the parameter a.

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Q: d. lim f(x) e. lim f(x) c. lim f(x)

A: d.limx→2+f(x)= ?f(x)=2x ; x≥2limx→2+f(x)=limx→2+ 2x=2×2=4limx→2+f(x) =4e.limx→2-f(x) =?f(x)= x ; 1≤x...

Q: 2 Show that the following limit does not exist. lim Ty Cos y (r.9)-(0.0) 3r+ y²

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Q: Determine whether the alternating series converges. E(- 1*- k=3 7ln k k O The series diverges. O The...

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