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Calculus
Evaluate the double integral by polar coordinates. Integral D 8- 2x² - 2y²dA,
Calculus
Find the total mass of the given rod and the center of mass.
1. The length of a rod is 6 m and the linear density of the rod at a point x meters from one end is (2x + 3) kg/m.
2. The length of a rod is 9 in. and the linear density of the rod at a point x inches from one end is (4x + 1) slugs/in.
3. The length of a rod is 12 cm, and the measure of the linear density at a point is a linear function of the measure of the distance from the left end of the rod. The linear density at the left end is 3 g/cm and at the right end is 4 g/cm.
4. The measure of the linear density at any point of a rod 6 m long varies directly as the distance from the point to an external point in the line of the rod and 4 m from an end, where the density is 3 kg/m.
5. The measure of the linear density at a point of a rod varies directly as the third power of the measure of the distance of the point from one end. The length of the rod is 4 ft and the linear density is 2 slugs/ft at the center.
1. The length of a rod is 6 m and the linear density of the rod at a point x meters from one end is (2x + 3) kg/m.
2. The length of a rod is 9 in. and the linear density of the rod at a point x inches from one end is (4x + 1) slugs/in.
3. The length of a rod is 12 cm, and the measure of the linear density at a point is a linear function of the measure of the distance from the left end of the rod. The linear density at the left end is 3 g/cm and at the right end is 4 g/cm.
4. The measure of the linear density at any point of a rod 6 m long varies directly as the distance from the point to an external point in the line of the rod and 4 m from an end, where the density is 3 kg/m.
5. The measure of the linear density at a point of a rod varies directly as the third power of the measure of the distance of the point from one end. The length of the rod is 4 ft and the linear density is 2 slugs/ft at the center.
Calculus
Find the length of the curve given by x = t
Calculus
if f(x)= sin⁻
Calculus
please do this question as it is very urgwnt for me and for my assignments.
Trace the curve y = 8/(4-x^2) and state all the properties you use to trace it.
Trace the curve y = 8/(4-x^2) and state all the properties you use to trace it.
Calculus
Which of the following statements are true and which are false? Give reasons for your
answers, in the form of a short proof or a counter example.
(i) The function f defined by f(x) = tan(2x) is a periodic function with period π.
(ii) The function f: R---> R defined by f(x) = 1-|x| is differentiable at x=1
(iii) The function f: [3,4] ----> R defined by
f(x) = x
answers, in the form of a short proof or a counter example.
(i) The function f defined by f(x) = tan(2x) is a periodic function with period π.
(ii) The function f: R---> R defined by f(x) = 1-|x| is differentiable at x=1
(iii) The function f: [3,4] ----> R defined by
f(x) = x
Calculus
. Find the area included between
x^2+y^2= 4x
and
y^2=x
above x-axis
x^2+y^2= 4x
and
y^2=x
above x-axis
Calculus
A spherical balloon is deflated so that its volume is decreasing at a rate of 3 ftଷ/min. How fast is the diameter of the balloon decreasing when the radius is 2 ft?
Calculus
Let 𝑓 be a function which is everywhere differentiable and for which 𝑓(2) = −3 and 𝑓 ′ (𝑥) = √𝑥 2 + 5. Given that 𝑔 is defined such that 𝑔(𝑥) = 𝑥 2𝑓 ( 𝑥 𝑥 − 1 ), show that 𝑔 ′ (2) = −24.
Calculus
Differentiate the following functions (i) If 𝑦 = 𝑒 −3𝑡 sin 4𝑡, prove that 𝑑 2𝑦 𝑑𝑥 2 + 6 𝑑𝑦 𝑑𝑥 + 2𝑦 = 0. (ii) Given that sin(𝑥 2 + 𝑦) = 𝑦 2 (3𝑥 + 1), show that 𝑑𝑦 𝑑𝑥 = 2𝑥 cos(𝑥 2 + 𝑦) − 3𝑦 2 2𝑦(3𝑥 + 1) − cos(𝑥 2 + 𝑦
