5) Write the equation of the line through the points P(1,3,7) and Q(2,5,11) in: a) Vector form b) Parametric form c) Symmetric form

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A: We have to solve  part 1, 2 and 3.

Q: Determine

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A: Topic:-  limit calculus

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A: Verify the identity

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Q: 3~5 3 31 ㄱ 2 2 7) 51-³

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Q: 4. Consider the sequence {n} (a) Write out the first five terms of the sequence (b) Determine…

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Q: ƒ(z) = (z³ + z − 4); [−1,2] x h(x) ; [0,2] x-3'

A: Mean Value Theorem:  f'(c) = (f(b)-f(a))/(b-a)

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Q: NA AN 4 » *K 0

A: We have to graph the hyperbola

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Q: The solution set of the equation x2=12-4x is {2,6} صواب خطأ

A: The given equation is: x2=12-4x  ...(1)

Q: 13. Convert the rectangular equation to polar form. 1+1=2

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A: Given; f(x)=(5x2-4x3)3(secx+tanx)3.

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Q: 6. Find 0²y of z = In(xy)

A: We can find the partial derivative as below.

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Q: lim x-0 1+x−1

A: Given problem:-

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A: Velocity

Q: Solid S is bounded by the given surfaces. (1) Sketch S and label it with its boundaries. (2) Give…

A: Given problem:- Solid S is bounded by the given surfaces. (1) Sketch S and label it with its…

Q: = (x² + y² + z²) −½, then + + 8²v მ2u 8² 8x² მ2 82² If v=

A: v=x2+y2+z2-12 Now,  ∂v∂x=∂x2+y2+z2-12∂x       =∂x2+y2+z2-12∂x2+y2+z2×∂x2+y2+z2∂x…

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Q: a²z Find of z = In(xy) a²y

A: To find out the double partial derivative with respect to y

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Q: A force of 6 pounds is required to hold a spring stretched 0.2 feet beyond its natural length. How…

A: F = -kx  6 = -k(0.2) So, k = 30   Work done, W = (1/2)kx2 = (1/2)*(30)*(0.9)2 = 12.15

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Q: 1 Lim x→0* x0x 1 sin x

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Q: Find the derivative of the function at Po in the direction of A. 0 f(x,y,z) = xy + yz+zx,…

A: Given query is to find direction derivative.

Q: II. Solve the following problems. Enclose final answer. 9. A gutter with trapezoidal cross section…

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Q: SOLUTION

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Q: Numerical Integration: 1 √x 1. 0 dx

A: We can find the solution of the definite integral as below.

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A: z=x-yx+y differentiate partially with respect to x

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Q: 1. For questions A and Given: Radium decomposed at a rate proportional to the qualit of radium…

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