QUESTION 1 By using the method that you have been taught in this course, evaluate the following multiple integrals by using cylindrical coordinate. You MUST support your answer with a proper figure of the solid, G and its projection on xy-plane. G where: G is the solid bounded below by xy-plane and above by z = 4-x² – y²

Q: By using double integrals, find the area of the regions enclosed by a) curves y = y=-x², lines x =…

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Q: 4. By using double integrals, find the volume of the solid enclosed by paraboloid z = 16– x² – y'…

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Q: Express the given equations in polar coordinates (а) х%3D3 (b) x² + y = 7 (c) x² + y² +6y = 0 (d)…

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Q: Sketch a few level curves of the following functions. (i) f(x, y)=y-x (ii) f(x,y)= Use the level…

A: We have given equation of curve, we need to sketch level curves.

Q: Calculus-Sharel - Google Sheets

A: Consider: x+2x-4≥1. Solve for x. Subtract 1 both sides. x+2x-4-1≥1-1x+2-x-4x-4≥0x+2-x+4x-4≥06x-4≥0

Q: Determine lim a,n of the sequence (an) where n00 4 – 2n + 6n² an Зп? + п — 4

A: Given sequence is, an=4-2n+6n23n2+n-4 Now, limn→∞6n2-2n+43n2+n-4=limn→∞6-2n+4n23+1n-4n2=6-0+03+0-0 […

Q: 2. Equation is given in spherical coordinates. Express the equation in rectangular coordinates and…

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Q: soùd lines For Portions dash ùnes of borndry included in thee bmain and not include Suot1 For d)…

A: We are asked to find the domain of the function.

Q: Find the slope and concavity (if possible) at the given value of the parameter. x(0) = 2 + sec(0),…

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Q: (x+h)? – 2(x+h) – 3-(x²-2x-3). lim 2. Use the limit definition to evaluate

A: Given that limh→0 x+h2-2x+h-3-x2-2x-3h. Compute the limit as follows.

Q: 9. Find the vector triple product of vectors u, v and w. =(2,-1,3), v=(0,1,7), w=(1,4,5) (a) ux(vxw)…

A: The solution of the problem is given in the next steps.

Q: Graph the following: (a) Graph f(x)=2-1 by generating a table of values. (b) Graph the function f(x)…

A: Exponential function: A function which is represented in the form fx=ax for some positive constant a…

Q: 8. Show that jxk i.jxk (а) і— kxi (b) j= i.jxk ixj (c) k =- i.jxk

A: Topic = Vector

Q: What are the solutions to the system of conics? *- = 1 x2 4 2 y? = 8 (x + 1) Drag the ordered pairs…

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Q: 1. Perform the stated operations on the vectors u, v and w. u = 3i – k, v=i-j+2k, w = 3j (а) w- v…

A: Using addition & subtraction of vectors. Adding & subtracting same component's.

Q: Find the domain and the range For the to llowin g function ? E)FC×リ: メy F)FCx,y)ン +! x-2コ す)F(xy):…

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Q: Sketch the region of integration corresponding to the integral 6x-x² 5(2² + y*)y dydx and compute…

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