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tà ¢ 0
e
t à ¢ 1
t
= 1 to show from first principle that
d
dx(2e
2x à ¢ e
à ¢ x + 5x) = 4e
2x + e
à ¢ x + 5.
[
a) Show that f is continuous at x = 5. [8]
b) Show that f is not differentiable at x = 5. [6]
limxà ¢ a
x
2 Ã ¢ 2ax = Ã ¢ a
2
.
Question 01
The accompanying figure shows the position versus time curve for a certain particle moving along a straight line.
Estimate each of the following from the graph:
(a) the average velocity over the interval 0 ≤ t ≤ 3
(b) the values of t at which the instantaneous velocity is zero
(c) the values of t at which the instantaneous velocity is either a maximum or a minimum
(d) the instantaneous velocity when t = 3 s.
In the temperature range between 0
0C and 7000C the resistance R [in ohms] of a certain platinum resistance
thermometer is given by
R = 10 + 0.04124T − 1.779 × 10−5T
2
where T is the temperature in degrees Celsius. Where in the interval from 0
0C to 7000C is the resistance of the
thermometer most sensitive and least sensitive to temperature changes? [Hint: Consider the size of dR/dT in the
interval 0 ≤ T ≤ 700.].
In the temperature range between 0 C and 7000C the resistance R [in ohms] of a certain platinum resistance thermometer is given by
R = 10 + 0.04124T − 1.779 × 10−5T2
where T is the temperature in degrees Celsius. Where in the interval from 0C to 700C is the resistance of the thermometer most sensitive and least sensitive to temperature changes? [Hint: Consider the size of dR/dT in the
interval 0 ≤ T ≤ 700.].
thermometer is given by
R = 10 + 0.04124T - 1.779 * 10 ^ - 5 * T ^ 2 where 7 is the temperature in degrees Celsius. Where in the interval from 0 °C to 700 ^ 0 * C is the resistance of the thermometer most sensitive and least sensitive to temperature changes? [/lint: Consider the size of dR / d * T in the interval 0 <= T <= 700.1
find all second partial derivatives of
f(xy)=xcosy+ye^x
During the first 40s of a rocket’s flight, the rocket is propelled straight up so that in t seconds it reaches a height of
s = 0.3t
3
ft.
(a) How high does the rocket travel in 40s?
(b) What is the average velocity of the rocket during the first 40s?
(c) What is the average velocity of the rocket during the first 1000 ft of its flight?
(d) What is the instantaneous velocity of the rocket at the end of 40s?
