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Q: What is the point at which the lines x = 3 - t, y = 2 + t, z = 5t intersects with x - y + 2z = 9 ? О…

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Q: Find the arc length of the parametric curve. 4 cos(t), y = 4 sin(t), z = 3t; 0<t<T L=

A: Here we have to find the arc length of the parametric curve.

Q: Find the area of the region bounded by the given equations. Clearly state the integral(s) used to…

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Q: 1 Find the length of the curve y (x2 + 2)3/2 from x = 0 to x =9. 3

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Q: 2. Find an equation of the plane containing the point P (0,-.) and the line determined by the two…

A: Equation of a plane P containing a line of intersection of two planes P1,P2 is given by, P=P1+λP2

Q: 8.) A box with a square base and no top must have a surface area of 48 square inches. Find the…

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Q: Activity 1.5.2. A potato is placed in an oven, and the potato's temperature F (in de- grees…

A: Solution: Given data

Q: Activity 1.5.3. A company manufactures rope, and the total cost of producing r feet of rope is C(r)…

A: A company manufactures rope, and the total cost of producing r feet of rope is Cr dollars.To…

Q: 1) What are the equations (4 of them) that show the relationship between polar and rectangular…

A: We can solve as follows

Q: Match the vector field with its graph. F(x, y) = yi -6+ 世 -5+

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Q: Find the first three nonzero terms in Maclaurin Series for each function

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Q: Describe the graph of the equation. r = 3cos ti - 4 sin tj +k O An ellipse in the plane x = 1,…

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Q: Matching Type. Match the functions in Column A with their corresponding derivatives in Column B.…

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Q: Find V · (V × F) if F(x, y, z) = 10 sin xi + 7 cos(9x – 10y)j + 3zk. V·(V × F)

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Q: Describe the domain and range of the function. KX, y) = 9x2 - y

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Q: 5x + 2lnx 8. lim X+3Inx

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Q: Verify Green's Theorem by evaluating both integrals ƏN dA y? dx + x² dy = ay for the given path. C:…

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Q: Consider the following functions. 3 f(x) = Vx - - 3 3 g(x) = x – 3 Sketch the region bounded by the…

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Q: Find the limit. NOTE: Enter the answer using round brackets. t2 + 4 1 lim t→+∞ \ 3t2 +4' 2t (?, ?)

A: The given limit ; limt→+∞t2+43t2+4,12t

Q: Sol V= cotcex) dx /2

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Q: ) Find an equation of the line tangent to the curve y = x²e²-3 at a = 3.

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Q: Use the figures to evaluate the function if f(x) = sin x. (x,1) f(a + B)

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Q: 4) Find the critical points of the parametric equations x = t* – 1 y = t3 -t

A: Topic:- application of derivatives

Q: d d. Calculate ri(t) - r2(t)] and ri(t) x r2(t)] first by differentiating dt the product directly…

A: r1(t)=9t i +9t2 j+6t3 kdr1dt=9 i +18t j +18t2 kr2(t)=t4 kdr2dt=4t3 kr1(t)·dr2dt=(9t, 9t2, 6t3)·(0,…

Q: 2x 1- cos x Graph f(x) = sin for Osxs2x by using transformations. 2 2- Use the graphing tool to…

A: To find: the graph of sin2x2 = 1-cosx2 for 0≤x≤2π Graph of cosx will be as following

Q: Calculus

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Q: Starting from the same point, Reden starts walking eastward at 60 cm/s while Neil starts running…

A: To find out the rate of change if distance between Reden and Neil after 2 seconds.

Q: -z“, where T is The temperature at a point (x, y, z) is given by T(x,y, z) = 200e measured in…

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Q: nance. A person wishes to have $27,100 cash for a new car 4 years from now. How much should be…

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Q: Evaluate the double integral over the rectangular region R. 4xy dA; R = {(x, y): – 1 < x < 1, – 6 <…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Evaluate the integral using the following values. x dx = 60 x dx = 6, dx = 2 J2 %3D 5x dx J2

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Q: dx хV х2+2х-1

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Q: Solve the initial value problemy-10y +50v-0 for y(0)-1 andy (0)-5. After getting the equation for…

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Q: 1) Find and of the following equation then simplify whenever possible. dx x = 2u* – u3 + u – 11 , y…

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Q: 5- ý = 4x+3y+2 3xt2yt1

A: This is a problem of differential equation. Based on the homogeneous system of equation concept we…

Q: In x 6. lim, x

A: Solution:

Q: esing pyphagoras th, Diff wt to t 2xda +rydy 20 at da dt az3 m

A: Apologies for the inconvenience.   Let, x = the distance from the wall. y = the height of the top of…

Q: d²y of the following equation then simplify whenever possible. 3) Find and dx dx- x = 3em y = 4e-m

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Q: 10 sin () sin(a da

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Q: Find the measure of the angle a ircle. 13. (플,-)

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Q: QUESTION 3 Three machines turn out all the products in a factory, with the first machine producing…

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Q: Зх +1 a) y =- 1 b) g(x)= Jx -

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Q: 3. Find a set of symmetric and parametric equations of the line passing through the point (1, 4, 2)…

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Q: 10 10 If f(x) dx = 19 and f(x) dx = 6, find the following. %3D f(x) dx

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Q: Evaluate the definite integral. Using Fundamental Theorems of Calculus. (x?2 - х) dx x2 + x +1

A: ∫01x2-xx2+x+1dxit is a improper fraction ( degree of Numerator= Degree of denominator)Using long…

Q: Use a double integral to find the volume of the region under the graph of f(x, y) = xy and above the…

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Q: | (2x - y) dx + (x + 7y) dy. Evaluate C: x-axis from (0, 0) to (0, -7) and (0, -7) to (4, -7)

A: x-axis from 0,0 to 0,-7 indicates that interval of y is from 0 to -7 y-axis from 0,-7 to 4,-7…

Q: Show that the differential form in the integral below is exact. Then evaluate the integral. (-2,4, -…

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Q: cosxdx 3T +Sinx

A: