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: Differentiate the function. dy dx y = (9x2 - 2) (8x2 - 2x+6) =

A: The given function is y=(9x2-2)(8x2-2x+6)   To find: The derivative dydx=?

Q: What are the coordinates of the points in the graph of y? – x² + 6x – 13 = 0 in which the tangent…

A: y2-x2+6x-13=0 --------------(1) Differentiating with respect to x ddxy2-x2+6x-13=ddx(0)…

Q: Determine Dx[x(x-2)²]

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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: dy Ex2: find for the following functions: dx a) y = (x² + 1)5 b) y = [(5-x)(4- 2x)]? c) y = (2x3 –…

A: According to guidelines we should have been able to solve only three subpart of the question

Q: x² – 10x – 5 dx |x- 1)-(x² + 1)

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Q: Find the length of the curve defined by

A: Length of the curve is :y=3x3/2 -11Differntiation :dy/dx= 3 * 3/2 *x3/2-1dy/dx= 9/2 *x1/2(dy/dx)2…

Q: (c) Find an equation of the tangent line to the graph of x2/3 + y2/3 = 5 at the point (1,8).

A: Given: The equation of the graph is  x23 + y23 = 5 To find: The equation of the tangent line to the…

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: Find all the points on the graph of (x² + y²)² = x² – y² that have vertical tangent line.

A: This question is taken from the tangent and line in which we have to all points on the graph that…

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

Q: Use the sign pattern for the derivative dƒ/ dx = 6(x - 1)(x - 2)^2(x - 3)^3(x - 4)^4 to identify the…

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