Все публикации

0:04:45

Tangent Line | Implicit Differentiation | Find the tangent line for xy+2=3x^2-y at x=0.

0:04:32

Continuity of a Function | ε-δ | Prove that for f(x)=x^2, f is uniformly continuous on [0,3].

0:04:38

Euclid’s Division Lemma | Write the gcd of 15 and 22 as a linear combination of 15 and 22.

0:06:38

Intersecting, Parallel, & Skew Lines | Do L1 and L2 intersect?

0:04:33

Epsilon-Delta Limit Proof | Use ε-δ to prove lim (2x^2-7x+3) / (x-3) = 5 .

0:03:11

Vector Projection | Project the vector [1,2,3] onto the vector [1,1,1].

0:07:49

Monotone Sequences | (1) Show that {xj} is increasing and bounded above. (2) What is the limit?

0:04:17

Equation of a Sphere | Find the center and the radius of the sphere x^2+y^2+z^2+4x-6y+2z+6=0

0:07:12

ε-δ Limit Proof | Use ε-δ definition to prove lim (3x^2-5)=7

0:04:39

Curvature | Find the curvature of r(t)=[t, 2t^2, 1/3t^3] at the point t=2.

0:06:33

Uniform Distribution | Compute expectation of the insurance payment and the unreimbursed portion.

0:07:09

Moment Generating Function | Given the exponential distribution f(x)=3e^-3x find the MGF.

0:07:55

Conditional Variance | Find Var(X|Y=1) and Find Var(1/X+1| Y is even).

0:06:17

Lagrange Multipliers | Find the extreme values of f(x,y)=2x^2+y^2 constrained to x^2+y^2=16.

0:04:29

Torsion | Find the torsion of r(t)=[t, t^2, t^3] as of function of t.

0:07:58

Part 2 | Continuity of a Function | ϵ-δ | Prove f(x) is continuous at x=3.

0:07:37

Part 1 | Continuity of a Function | ϵ-δ | Prove the piecewise f(x) is continuous at x=0.

0:06:20

Motion Vectors | Given r(t) at t=0, find tangent and normal acceleration with velocity and speed.

0:04:44

Convergence of a Sequence | Prove the sequence bj=(-1)^j does not converge.

0:06:52

Subgroups | Prove H is a subgroup of G.

0:05:04

Binomial Expansion | What is the binomial expansion of (2x-3)^5?

0:04:56

Part 3 | Continuity of a Function | Prove f(x) is discontinuous at x≠0, x≠3

0:03:41

Spherical Coordinates | Derive the volume of a sphere using triple integrals in spherical coordinate

0:05:45

Polar Area | Find the area of one leaf of the petal curve r=3sin(3theta).