5. I hold a pencil 1 mm from my right eye, and slowly move it away. Its distance from my eye after t seconds is d(t) = 1+t mm. As the pencil moves away, my eye will automatically adjust to remain focussed on it. In particular, the focal length of my eye (also measured in mm) when the pencil is d mm away is 25d f(d) = 25 + d Find 4, the rate at which my eye's focal length is changing with respect to time.

Q: fx) D, f(쪽) -1, and f(플) %=D1, and COSX 3 f) = -1. Find S f(x) dx. %3D

A: Given that  f'x=cosxx, fπ2=-1 and f3π2=1find ∫π23π2fxdx

Q: QUESTION 8 Differentiate. y = 6x-4 dy dx 4x (6x - 4)2 dy dx 4 бх - 4 dy O dx 4 (6x - 4)2 dy 12x-4…

A:

Q: (3y? + 2)2 = 1 and y(-1) = 1 What is x when y = 2? %3D dx

A: solve the differential equation by separating the variable and integrate it.

Q: A3) Find the equation of the line tangent to the graph of f(x) = 4x³ + 3x? – 2x – 8 at x = -2.

A:

Q: MA 1. Find the following, a. f(5x2 – 6x +3)dx = OWI +2 4t %3D dt

A:

Q: Set up two different ways to find the shaded area - one way oriented horizontally, with a “dx”, the…

A: Sol:By considering small differential area, dy,f(x) = 3⋅ xg(x) = 32 ⋅ x-1x1 = f-1(y) = y23 andx2 =…

Q: Given the equation below, find 38x5 +10x⁹5y + yº 95 9 dy dx = y = = 49 dy da Now, find the equation…

A:

Q: Integrate the following functions [(-2x² – 9x – 7)dx [(4x° – 9)* (20x“ )dx. i. ii. ji.

A:

Q: Find the tangent equation for the function: f(x) = Vx2 + 5 at x-2?

A:

Q: Determine the value of- dy - at (0,0) for the following expression: 3x² +2y = 3x – 2y dx 10.

A:

Q: 4. A penny is dropped from the top of the tallest radio tower in the U.S., the KVLY-TV tower in…

A: Here we use derivatives to solve this problem.

Q: b) Solve the following D.E to find y as a function of x: -3y=1-x²..

A:

Q: mark all the points on the plot below where dy/dx=-2

A:

Q: Find p, q if f," f(x) dx – f" f(x) dx = [i s(x) dx. (Give your answers as whole or exact numbers.) p…

A:

Q: O Find (a) |VT-x)/x dx, (c) (4-x*y² dx. Ans, ía) 1/60, (/) x/2. (c) 31

A:

Q: a) Integrate the following functions i. (-2x² – 9x – 7)dx (4x* – 9)* (20x“ )dx. [-4e"dx ii. iii.

A:

Q: SSx = 172.5, SSY = 80.6, and ∑[(X – Mx) (Y – MY)] = 95.33, r =  A. .08. B. .01 C. –.81. D. .81.

A: SSx = 172.5 SSY = 80.6 and ∑[(X – Mx) (Y – MY)] = 95.33

Q: Q4) Find for the following functions (- dx Зх +4 %3D 2x+3 6. y = tan-1 V4x3 - 3 %3D

A:

Q: (2x+7)2 x 2 dx

A: on diffrentiating this with respect to x we get =2(2x+7)ddx(2x+7)=2(2x+7)×2=4(2x+7)

Q: V27x° dx

A: Using power function formula of integration.

Q: If f(x) = 2x2 - 9x + 4, find the equation of the line tangent at a 2. %3D

A: Given that: f(x) = 2x2-9x+4  To find:  Equation of tangent line at x=2.