18.Water is flowing into a cylinder tank at the rate of 2 m3/min. If radius of tank is 0.5 m. How fast is the surface of the liquid rising?

Q: 19. Does the line that is tangent to the curve y = x3 at the point (1, 1) intersect the curve at any…

A:

Q: 5. Find an equation of the line tangent to the curve y = 3x² 1 and parallel to the line 2x – y + 3 =…

A: Explained below

Q: Find the line tangent to the curve x + y3 = 4 at the point (3/3, –1).

A:

Q: t this problem?

A: Consider the given parabola:

Q: How do you find the equation of the tangent line to the parabola for y = x2 − 3x − 1 at x = 4.

A: The equation of the given parabola is y=x2-3x-1. We have to find the equation of the tangent line to…

Q: A swimming pool with a rectangular surface 22.0 m long and 9.0 m wide is being filled at the rate of…

A:

Q: 5. Hance sits at one of the points on the curve y = 2x³ -3x²-12x +20 where the tangent is parallel…

A: Please see the below picture for detailed solution.

Q: FInd a so that the curve y = x3+ ax2+ 44 will have a relative extrema at (2,5). Find other extrema…

A: The given curve is y=x3+ax2+44. Since the curve has a relative extrema at (2,5), x=2 is a critical…

Q: Find the point (xo, yo) on the graph of y = x' + 9x² + 6x – 3, at which the slope of the tangent…

A:

Q: 12. The line y = 8x + b is tangent to the curve y = 2x². Determine the point of tangency and the…

A:

Q: Make the curve y= ax2+bx+c pass through (2,1) and be tangent to the lane y= 2x +4 at (1,6)

A: The given curve passes through (2,1) ⇒1=4a+2b+c                                    (1) And the curve…

Q: Find the length of the curve y=lnx from x=1.5 to x=3.

A:

Q: Find the length of the curve defined by y = 3z3/2 - 3 from x = 3 to a = 9. The length is

A:

Q: 17. Given the curve y = 3x³ – 4x² +7, find the slope of the tangent line at the point when x= 3.

A:

Q: Find the point (xo,yo) on the graph of y = x' + 9x² + 7x – 5, at which the slope of the tangent line…

A:

Q: An inner-city revitalization zone is a rectangle that is twice as long as it is wide. The width of…

A:

Q: Show that the curve of y = 2e2z + 3r + 2r3 has no tangent line with slope 2.

A: The given curve is y=2e2x+3x+2x3. Obtain first derivative as follows. dydx=ddx2e2x+3x+2x3=4e2x+3+6x2

Q: 2. What is the slope of the line tangent to the curve 8x³ – y² = 4 at the point (1,-2)? 3. What is…

A: Since first subparts question statement missed. Answer 2 and 3

Q: Find the point (xo, yo) on the graph of y = x + 3x² + 4x – 5, at which the slope of the tangent line…

A:

Q: At which points on the curve y = 1 + 60x3 - 2x5 does the tangent line have the largest slope? 1 5…

A:

Q: 3- If the value of elasticity is equal to Ey = 0.21 then the ., note that 11.5 = xi = 10, yi %3D…

A:

Q: 20. Does the line that is normal to the curve y = x² + 2x - 3 at the point (1, 0) intersect the…

A:

Q: An input-output curve of a 10 MW station is expressed as follows: |= 10°(10+8L+0.4L?) where / is in…

A: An input-output curve of a 10MW station is expressed as I=10610+8L+0.4L2

Q: At what point on the parabola y =  3 x2+ 2x is the tangent line parallel to the line y = 10x −2? Use…

A: First prinicipal : dydx=limh→0f(x+h)-f(x)h

Q: A swimming pool with a rectangular surface 21.0 m long and 15.0 m wide is being filed at the rate of…

A: To calculate the rate of changing of height when the depth of the water at the deep end is 0.8m

Q: 8. Find the point on the curve y = √2x 3 from the point (1, 4)-

A:

Q: How fast does the  slope of the curve y= (x2+x+1)2 change at the point where x=2

A: First derivative of a function represents the change in function or slope of the function and second…

Q: Suppose a model for the surface area of a human body is given by S = 0.1094w0.425,0.725, where w is…

A:

Q: find the length of the curve 3y2=4x3 from x=0 to x=8 when y greater than or equal to 0.

A: The formula for length of a curve f(x) extending from point a to point b is given as,

Q: 8. What is the rate of change of the slope of the tangent line to the curve y =x – 3x2 +1 when x =…

A:

Q: B. Find the length of the curve y = x² from x 0 tox = 4.

A:

Q: 2. Find the length of the curve y=- 1 from 1<x<2. 8 4x?

A:

Q: 2. Find the slope of the tangent to the curve y = 3 + 4x² − 2x³ at the point where x = a -

A: The equation of the curve is given by y = 3+4x2-2x3 To evaluate: The slope of the tangent to the…

Q: 25. Find the equation of the line tangent to the curve x2 + y2 = 1 through the point (,).

A:

Q: Make the curve y=ax²+bx+ c pass through (2,1) and be tangent to the line y=2x+4 at (1,6)

A:

Q: (3) Find an equation of the tangent line to the curve y = 2x² + 3 that is parallel to the line %3D…

A:

Q: Determine the critical points of the curve y = x³ – 5x2 - 36 x + 25.

A:

Q: The line that is normal to the curve x + 3xy - 4y² = 0 at (3,3) intersects the curve at what other…

A: Given: x2+3xy-4y2=0 at (3,3)

Q: 4) Find an equation to the line tangent to y = 5 + |x – 2| at the coordinate (2, 5).

A:

Q: please show in your solution how to get the pt of intersection between curves  y=(x)^1/3 and…

A: Point of intersection of the curves is the point where two curve intersect .

Q: At what points on the given curve x = 2t3, y = 4 + 8t - 11t2 does the tangent line have slope 1?…

A:

Q: 5. Find the point on the parabola y=-x+3x+4 where the slope of the tangent line is 5.

A:

Q: What is the equation of the line that crosses the y-axis at 2 and h. a unit rate of ?

A: We have to find the equation of the required line. The required line crosses the y axis at 2, that…

Q: For the given curve y = 5x – 2x', when x increases at the rate of 2 units / sec, then how fast is…

A:

Q: 12)What is the slope at (1,2) for curve define by xy^2=4?

A:

Q: 5. Find the point on the parabola y=2x-3x+6 where the tangent line is parallel to the line 7x+y=1.

A:

Q: 1) Find the slope of the line tangent to the graph of y=x²+1at(2, 5).

A:

Q: The curve y = ax² + bx+c passes through the point (3,6). The line y = 4x + 1 is tangent to the curve…

A:

Q: Find the point (xo, yo) on the graph of y = x' + 9x² + 7x – 5, at which the slope of the tangent…

A:

Q: At what point on the parabola y=3x^2+2x is the tangent line parallel to the line y=10x-2? Use first…

A: We have to find the point.