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Calculus
Find the volume inside the sphere x^2 + y^2 + z^2 =16 and outside the cylinder x^2 + y^2 =4.
Calculus
Find all points where f fails to be differentiable. Justify your answer. Also draw the graph of f(x) by using
MATLAB.
(a) f(x) = |3x − 2| (b) f(x) = |x
2 −2|
Calculus
n each part, compute à °
à ¢ ²
, Ã °
à ¢ ²Ã ¢ ²
, Ã °
à ¢ ²Ã ¢ ²Ã ¢ ² and then state the formula for nth derivative à °
(Ã ° )
(a) Ã ° (Ã ° ¥) = Ã °
2Ã ° ¥
(b) Ã ° (Ã ° ¥) = Ã ° Ã ° Ã ° 3Ã ° ¥
(c) Ã ° (Ã ° ¥) = Ã ° Ã ° Ã ° ¥
Draw the graph of first three derivatives of à ° (à ° ¥).
à ¢ ²
, Ã °
à ¢ ²Ã ¢ ²
, Ã °
à ¢ ²Ã ¢ ²Ã ¢ ² and then state the formula for nth derivative à °
(Ã ° )
(a) Ã ° (Ã ° ¥) = Ã °
2Ã ° ¥
(b) Ã ° (Ã ° ¥) = Ã ° Ã ° Ã ° 3Ã ° ¥
(c) Ã ° (Ã ° ¥) = Ã ° Ã ° Ã ° ¥
Draw the graph of first three derivatives of à ° (à ° ¥).
Calculus
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 Ã ¢ 1.779 Ã 10Ã ¢ 5Ã ° 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 Ã ¢ ¤ T Ã ¢ ¤ 700
Calculus
Use the precise def i nition of a limit (à µ à ¢ à ´ method) to show that lim xà ¢ a x2à ¢ 2ax = à ¢ a2. [7]
Calculus
Second order derivative of (log x-x) is
Calculus
Find all points where f fails to be differentiable. Justify your answer. Also draw the graph of f(x) by using
MATLAB.
(a) f(x) = |3x − 2| (b) f(x) = |x
2 −2|
Calculus
In each part, compute f
′
, f
′′
, f
′′′ and then state the formula for nth derivative f
(n)
(a) f(x) = e
2x
(b) f(x) = sin3x
(c) f(x) = lnx
Draw the graph of first three derivatives of f(x).
Calculus
Use the fact that lim
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.
[
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.
[
Calculus
Let f(x) = |2x à ¢ 10| + 2 .
a) Show that f is continuous at x = 5. [8]
b) Show that f is not differentiable at x = 5. [6]
a) Show that f is continuous at x = 5. [8]
b) Show that f is not differentiable at x = 5. [6]
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#339914 on Dec 2023
#339914 on Dec 2023