Find the πth order differential coefficient of π¦ = sin π₯ log(ππ₯ + π).
xβ1/β3=yβ8/6=zβ3/β2Β Β Β Β andΒ Β Β Β xβ8/4=y+3/β5=zβ7/2
Β Β Β Β b.Β Give the equations of two lines that meet at the point (β1 5, 2) and which meet at right angles, but do not use that point in either of the equations. Explain your reasoning
The equation for the instantaneous voltage across a discharging capacitor is given by π£ = πππ β π‘ π , where ππ is the initial voltage and π is the time constant of the circuit. The tasks are to: a) Draw a graph of voltage against time for ππ = 12π and π = 2π , between π‘ = 0π and π‘ = 10π . b) Calculate the gradient at π‘ = 2π and π‘ = 4π . c) Differentiate π£ = 12π β π‘ 2 and calculate the value of ππ£ ππ‘ at π‘ = 2π and π‘ = 4π . d) Compare your answers for part b and part c. e) Calculate the second derivative of the instantaneous voltage ( π 2 π£ ππ‘2 ).
Find the position vector when acceleration a(t)= 2i + j + 3k
(A) A company's total revenues (in millions of dollars) t years from
now are predicted by R(t). Briefly explain what R(8) = 126.60
and R' (8) = 25.30 mean in the context of this question.
Order the following values from largest to smallest. In your work document provide aΒ briefΒ reasoning for your choices N'(-6), N' (0), N' (1), N' (2)
Graph the given curve and find the area of a bounded region.
x= 3y^2 - 9
Graph the given curve and find the area of a bounded region.
y= 4x - x^2
\int _3^6\:|12x-10|dx
Find the fourier integral for f(x)= C |x|<=1 and f(x)= 0 |x|> 1 we here C is constant