The Numbers Game

Tangent Line | Implicit Differentiation | Find the tangent line for xy+2=3x^2-y at x=0.
Tangent Line | Implicit Differentiation | Find the tangent line for xy+2=3x^2-y at x=0.
Continuity of a Function | ε-δ | Prove that for f(x)=x^2, f is uniformly continuous on [0,3].
Continuity of a Function | ε-δ | Prove that for f(x)=x^2, f is uniformly continuous on [0,3].
Euclid’s Division Lemma | Write the gcd of 15 and 22 as a linear combination of 15 and 22.
Euclid’s Division Lemma | Write the gcd of 15 and 22 as a linear combination of 15 and 22.
Intersecting, Parallel, & Skew Lines | Do L1 and L2 intersect?
Intersecting, Parallel, & Skew Lines | Do L1 and L2 intersect?
Epsilon-Delta Limit Proof | Use ε-δ to prove lim (2x^2-7x+3) / (x-3) = 5 .
Epsilon-Delta Limit Proof | Use ε-δ to prove lim (2x^2-7x+3) / (x-3) = 5 .
Vector Projection | Project the vector [1,2,3] onto the vector [1,1,1].
Vector Projection | Project the vector [1,2,3] onto the vector [1,1,1].
Monotone Sequences | (1) Show that {xj} is increasing and bounded above. (2) What is the limit?
Monotone Sequences | (1) Show that {xj} is increasing and bounded above. (2) What is the limit?
Equation of a Sphere | Find the center and the radius of the sphere x^2+y^2+z^2+4x-6y+2z+6=0
Equation of a Sphere | Find the center and the radius of the sphere x^2+y^2+z^2+4x-6y+2z+6=0
ε-δ Limit Proof | Use ε-δ definition to prove lim (3x^2-5)=7
ε-δ Limit Proof | Use ε-δ definition to prove lim (3x^2-5)=7
Curvature | Find the curvature of r(t)=[t, 2t^2, 1/3t^3] at the point t=2.
Curvature | Find the curvature of r(t)=[t, 2t^2, 1/3t^3] at the point t=2.
Uniform Distribution | Compute expectation of the insurance payment and the unreimbursed portion.
Uniform Distribution | Compute expectation of the insurance payment and the unreimbursed portion.
Moment Generating Function | Given the exponential distribution f(x)=3e^-3x find the MGF.
Moment Generating Function | Given the exponential distribution f(x)=3e^-3x find the MGF.
Conditional Variance | Find Var(X|Y=1) and Find Var(1/X+1| Y is even).
Conditional Variance | Find Var(X|Y=1) and Find Var(1/X+1| Y is even).
Lagrange Multipliers | Find the extreme values of f(x,y)=2x^2+y^2 constrained to x^2+y^2=16.
Lagrange Multipliers | Find the extreme values of f(x,y)=2x^2+y^2 constrained to x^2+y^2=16.
Torsion | Find the torsion of r(t)=[t, t^2, t^3] as of function of t.
Torsion | Find the torsion of r(t)=[t, t^2, t^3] as of function of t.
Part 2 | Continuity of a Function | ϵ-δ | Prove f(x) is continuous at x=3.
Part 2 | Continuity of a Function | ϵ-δ | Prove f(x) is continuous at x=3.
Part 1 | Continuity of a Function | ϵ-δ | Prove the piecewise f(x) is continuous at x=0.
Part 1 | Continuity of a Function | ϵ-δ | Prove the piecewise f(x) is continuous at x=0.
Motion Vectors | Given r(t) at t=0, find tangent and normal acceleration with velocity and speed.
Motion Vectors | Given r(t) at t=0, find tangent and normal acceleration with velocity and speed.
Convergence of a Sequence | Prove the sequence bj=(-1)^j does not converge.
Convergence of a Sequence | Prove the sequence bj=(-1)^j does not converge.
Subgroups | Prove H is a subgroup of G.
Subgroups | Prove H is a subgroup of G.
Binomial Expansion | What is the binomial expansion of (2x-3)^5?
Binomial Expansion | What is the binomial expansion of (2x-3)^5?
Part 3 | Continuity of a Function | Prove f(x) is discontinuous at x≠0, x≠3
Part 3 | Continuity of a Function | Prove f(x) is discontinuous at x≠0, x≠3
Spherical Coordinates | Derive the volume of a sphere using triple integrals in spherical coordinate
Spherical Coordinates | Derive the volume of a sphere using triple integrals in spherical coordinate
Polar Area | Find the area of one leaf of the petal curve r=3sin(3theta).
Polar Area | Find the area of one leaf of the petal curve r=3sin(3theta).
Green's Theorem | Evaluate the integral of a field in the region bounded by the rectangle.
Green's Theorem | Evaluate the integral of a field in the region bounded by the rectangle.
Reduced Echelon Form | 3 x 4 Matrix
Reduced Echelon Form | 3 x 4 Matrix
Preimage of a Set | Find preimages for (-9, ∞) and [0, 4)
Preimage of a Set | Find preimages for (-9, ∞) and [0, 4)
Linear Independence | Determine if the columns of matrix A are linearly independent.
Linear Independence | Determine if the columns of matrix A are linearly independent.
Proof by Induction | Prove 2^2n-1 is divisible by 3.
Proof by Induction | Prove 2^2n-1 is divisible by 3.
Finding the Unit Tangent & Principle Normal Vectors of a Curve
Finding the Unit Tangent & Principle Normal Vectors of a Curve