2. Find the volume of the parallelepiped having a = (1,4,–7), b = (2,–1,4) and c = (0,-9,18) as adjacent edges. What conclusion can you make about vector a, b and c ?

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A: Topic = Integration

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Q: b. Find all solutions, if any exist, by using Gauss – Jordan reduction method.

A: Follow the procedure given below.

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A: Here, the given curves are : y=sin x, y=0.2, y=-0.2

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Q: Find the area enclosed by one loop of the curve: r = 3sin(4theta)

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Q: Find a and b such that v = au + bw, where u = (1, 2) and w = (1, -1). v = (9, 3) a = b =

A: This question is based on vector form.

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Q: y = 4 + cze3x

A: We can eliminate the arbitrary constants in the following steps.

Q: Find the average value of f(x) = over the interval [2, 4]. (3x + 1)2

A: Given problem:- Find the average value of f(x) = x/((3x2 + 1)2 ) over the interval [2, 4].

Q: d) y = sinh(lnx)

A: As per your request I will solve d part

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A: Given problem:- (x2 + 6y2 ) dx -  4xydy = 0  Solve the given differential equation

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Q: Find the equation of the tangent line to the curve y = 6 sec z – 12 cos z at the point 6). The…

A: y'=secx-12cosx' =secxtanx+12sinx Slope = secπ3tanπ3+12sinπ3=83. So, we have possible equation of…

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Q: Find the area enclosed by the curves y=sin(x), y=cos⁡(x), and the two vertical lines x=0 and x=π/2

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Q: * =1+ ev-z+5 e + e+y Option 5 O None of the Choices C = xe + e-y C = xe-5 et-y - Option 2 Option 1 C…

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Q: cos (*) 2kT COS 3 Consider the series ak k! k=1 a) What is ak+1? ak+1 aktl? b) What is ak aR-1/a If…

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Q: Find the angle 0 between the vectors in radians and in degrees. i + sin 3. in)j, v = cos()i + sin()…

A: Given problem:-

Q: . Evaluate the limit of a function using the concept of Special Limits. et-1 t2-3t+5 + t2-1 1. lim t

A: Given that a limit problem and we solve this problem by using general property of limit.     Here i…

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Q: af If f(x, y) 3x+7y (3x-7y) then is given by: 42y (3x–7y)² 21y (3x–7y)² 42y (3x-7y)2 21y (3x-7y)² -

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Q: 7. What region R in the ry-plane minimizes the value of r + y? - 9dA? 8. Calculate the average value…

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Q: Match the integral expression on the left to its suitable transformation on the right, after using…

A: We will use substitution for integration.

Q: Let F(x) = f(x) + g(x)e* + h(x)e²× + C be the antiderivative of G(x) = (x + e*)² value of f(x) +…

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Q: Find the following using the table below. 12 3 4 f(z) | 2 3 1 4 f'(x) | 31 2 4 g(x) 3 4 2 1 g'(x) |…

A: Given data

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Q: representing all ellipses having its centers at the origin and transverse axis x. a " + (w/)*] + yw…

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Q: If x =0.71 and y = 0.67, then value of C in the xsin-(x) is V1-x2 antiderivative of F(x) =

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Q: Find the points on the curve where there is a horizontal tangent line: x = 5cos(t) ; y = t3 - 3t2 +…

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Q: Fór the functión f whósé graph is given, state the following. (a) lim f(x) X - 00 1 (b) lim f(x) X →…

A: consider the figure given below :

Q: Consider the following initial value problem. y" + 5y' + 6y = 0, y(0) = 3, y (0) = ß, where B> 0…

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Q: A table of values for f(x), g(x), f'(x), and g'(x) has been given. Ax) g(x) f'(x) | g'(x) 3 2 -5 1 2…

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Q: What is the equation of the vertical asymptote of f(x) = tan x where 0 < x < T А. х — 2 B. f(x) has…

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Q: a) Evaluate the following integrals: eta TT/2 sin5e do tan 0 + tam30

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Q: Determine the equation of the line that is tangent to y = elan (2x) at x = 8

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Q: I. Find the first derivative of the given function. 3 5. v = (1+ sin*y)

A: We can solve this as follows: