(a) Given a vector A =-i+ 2j – 2z in Cartesian coordinates, (i) sketch vector A, (ii) find its magnitudes, (iii) find the expression of the unit vector in the direction of A, and (iv) evaluate the angle that A makes with the z-axis.

Q: QI) Evaluate the integral dx dy using polar coordinate

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Q: Consider the following function and dosed interval. fx) = x2/3 - 1, [-27, 27] Is f continuous on the…

A: F(x) is not differentiable on (-27, 27)

Q: The limit represents a derivative f'(a). Find f and a. V3 sin (5 + h) lim 2 h→0 h (Express numbers…

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Q: Q2) Solve the D.E dy – (2x/1- y²)dx = 0

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Q: Determine the area of the circle whose center is at the origin and tangent to the parabola y = x2 -…

A: y=x2-100from the grapph attached, Parabola cuts X-axis at (10,0) and (-10,0)

Q: Substitute x = 120 and y = 160 in s = x + y. (Only positive values need to be considered.) %3D 2. +…

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Q: Q2) Solve the D.E dy - (2x/1-y2)dx 0

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Q: Q2) Solve the D.E dy – (2x/1- y²)dx = %3D

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Q: Question 18 Consider Evaluate O (9x4+6x)e (x3+y2) O (3x²+6x)e «³+y?) O (6x²+ 3x)e «³+y?) O (6r*+9x)e…

A: Topic = Derivative

Q: 6.Find all the first partial derivatives of each function x² – y² c. f(x,y) ху с. = d. f(x,y)=e* cos…

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Q: Evaluate the following integral using Partial Fractions Method: x3 + x2 y : dx x2 + x – 2

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Q: Consider the parametric curve defined by x=3+5t and y=1+3t Over which values of does the curve has a…

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Q: The shaded region R is bounded by the lines x = 0, y = 0, and the curve y = x² – 2x + 2 as shown in…

A: Here, the volume is: V=∫03π(y)2dx =π∫03x2-2x+22dx=π∫03(x-1)2+12dx

Q: 25s^2+202s+25. FACTOR THIS QUADRATIC EQUATION ACCURATELY.

A: 25s2+202s+25=0We know that solution of quadratics equation ax2+bx+c=0 is x=-b±b2-4ac2a Herea=25,…

Q: Q3) Evaluate triple integral f Lx - y²)dz dy dx.

A: The given problem is solved below in detail.

Q: Find the equations of the lines tangent and normal to the curve given by the parametric equations…

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Q: 3. The radius of a spherical balloon is increasing at the rate of 2 cm per minute. How fast is the…

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Q: Find the centroid of the region bounded by the parabola y= 8x and the line y=2x. O (0.8,2) O (1,4) O…

A: We need to find centroid of the region.

Q: If u.v.w are three vectors such that each is inclined at an angle of " with the other two, and that…

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Q: Consider the region bounded by the curve v= x2 - 1 and the x - axis over the interval [0,3]. Find…

A: The equation for the x-axis is y=0. Draw the given two curves.

Q: Find the volume of the solid that results when the shaded region is revolved about the indicated…

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Q: Find the value of c where lim(x) does not exist for the graph of the function shown below a. none of…

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Q: Q5) Find volume of body bounded by z? + y2 + x2 9.

A: Given that - x²+y²+z²=9 => (x-0)²+(y-0)²+(z-0)²=3² Clearly which is a sphere with radius,r= 3…

Q: Evaluate triple integral , dz dy dx.

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Q: 3 -1 3 0 Given F = show that: 19. –F" = (-F)" 20. (F")" = F m 2.

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Q: 8. If f (x,y,z) = 3x²y – xyz + y²z? _Ifind each of the following: f. (x, y, z) b. f, (0,1,2) а.

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Q: What is 2x4

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Q: (4x* – r*y +y*)dx + x*dy = 0.

A: Let's find.

Q: g(x) - tan(x)

A: The functions given are fx=x,gx=tanx. Formula used: Newton's Formula xn+1=xn-fxnf'xn

Q: Q5/ Use Linear Regression to fit the following data: 1 2 3 4 Y 4 9 10 10 9 3 n 00

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Q: Determine the equation of the tangent to the graph of y = [2~/x - x][1+ /x - x ] at the point (1,…

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Q: Find (a) if fx) = /x-a+1.

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Q: Let a = 2i - 3j and b= 2j + 3k. Compute for the following: (a + b) · (a – b) None of the choices -8

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Q: Q5) Find volume of body bounded by z² + y² + x² = 9.

A: Explanation of the answer is as follows

Q: Evaluate fs 2°ds O a. 2*(sln2 - 1) (In2)2 O b. 2(słn2 - 1) (In2)2 O C. 25 - 1) In2 O d. 2° (+ 1) +1)…

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Q: Q5) Find volume of body bounded by z = 0 from below and z = 4- y from above inside y = x2 ,y = 4.

A: Set up the triple integral and solve to get the desired volume.

Q: e1/n n2 n=1

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Q: e-2 1 Evaluate: e-3 xInx Oc -In 6 O d. In 6 2/3

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Q: Is Rolle's theorem valid for the function f(x) = Vi-x on the segment [-1,1]? a. No since the…

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Q: Consider the parametric curve defined by 1=3+5t and y=1+3 Over which values of doesthe curve has a…

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Q: 2. S dx I+,x

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Q: Q4/ solve the equation by Newton -Raphson Method: F(x) = x* – 5x³ + 65 , start at x =2 , accuracy…

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Q: Compute f'(a) using f'(a) = lim f(a + h) – f(@) or f'(a) = lim Tx) – J(d) for f(x) = 15x³, a = 2. or…

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Q: Consider Evaluate ( 3x² + 6x ) e *+2) (6x2+ 3x) e +y2) (6x+9x)e+y2) O (9x4+6x) e *+y2)

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Q: 1.) f (x) = 10x10 4.) f (x) = %3D 2.) f(x) = x² – 9 5.) f(x) = 2x² + Vx 3.) f (x) = –x5 – x-3 – - x

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Q: Given the set of parametric equations x = 2t2- 1 and y = 3t + 4, eliminate the parameter t and…

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Q: Is it a function? 4 12 yes or no -1 -3 -4 -5 -21 Explain. 1 -3 4 12 -2

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Q: Differentiate the following functions. Show your complete solutions and emphasize your final answer.…

A: 1) f(x)=25x    Differentiate with respect to x   f'(x)=252) f(x)=-4x5+2    Differentiate with…

Q: Which of the following yields the value 3187 (8r+7y)dudy (8r+7y)dydr (8r+7)dudy O none of the oices

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Q: Q3) Evaluate triple integral y(x2-y?)dz dx dy.

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