Which expression gives the length of the curve y = 4x from x=1 to x = 4 ? 4 (A) [ 4x°dx (B) |V1+4x dx 1 1 (C) V1+16x* dx (D) | V1+64x dx 1 1

Q: Find an equation of the straight line having slope 1/6 that is tangent to the curve y=√x+5.

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Q: 2. Find y in terms of x if = 6x² – 2x and the curve passes through the point (1, 5). -

A: We have to find the value of x if dydx=6x2-2x and the curve passes through the point (1,5).…

Q: Create a 3-D plot of the function sin(/x² + y²) Vx² + y² for -8 <x5 8 and –8 < x < 8.

A: Note: Here, we are considering -8 ≤ x ≤ 8 and -8 ≤ y ≤ 8 rather than -8 ≤ x ≤ 8 and -8 ≤ x ≤ 8. We…

Q: x² – 10x – 5 dx |x- 1)-(x² + 1)

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Q: Find the set of values of y=2x+k meets the curve y=1+2kx-x² at 2 distinct points?

A: Given: y=2x+kat 2 distinct points

Q: Evaluate the slope at the point (2, 0) for: y² + sin(y) = 3x² - 12

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Q: x2 - 10x - 5 dx J (x - 1)2(x² + 1)

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Q: Differentiate the function. y = (4x-11)2

A: Chain Rule of differentiation : dydx=dydu·dudx