Function as a Composition: Domain Calculations
What are the formulas for f+g, f-g, fg, and f/g, and the domains of the functions if f(x) = 3x - 2 and g(x) = |x|?
Calculus and Analysis
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Evaluation and calculation of delta z and a total differential.
(a) evaluate f(1,2) and f(1.05,2.1) and calculate delta z. (b) use total differential dz to approximate delta z using equation f(x,y) = xe^y
Evaluate f(x) and f(y) at the indicated point.
Evaluate fx and fy at the indicated point f(x,y)= arccos xy pt. (1,1)
Integration Denoted Function
Intergrate the follow function f(x)=(1+x^2)/(1+x^4)
Sine Cancellation Laws
Using Cancellation Laws and other methods solve the following problems: 1) arcsin(1) 2) sin(arcsin(1/3))
Finding Inverse of one-to-one Functions Rules and Example
Determine a set of rules for finding the inverse of a function and find the inverse of: f(x) = (x-2)/(x+2)
Evaluation of a Function
A certain rational function f(x) contains quadratic functions in both its numerator and denominator. Aside from that, we also know the folliwing things about f: f has a vertical asymptote at x=5 f has a single x-intercept of x=2 f is removably discontinous at x=1, lim as (x)approaches 1 of f(x)= -1/9 evaluate lim of f(
Application of antiderivatives
A rocket lifts off the surface of the earth with a constant acceleration of 20 m/sec.sq. How fast will the rocket be going 1 minute later? What I did: a=20 m/sec.sq. v=20t+C m/sec, 1 min. = 60 sec. Initial conditions: v=0 when t=0 At t=0, C=0 Speed = |v|=20(60)+0, or 1200 m/sec. Question: Is this correct, or am I leav
Calculating the radius of a hemisphere
Given that the volume of a hemisphere (half a sphere) of radius r is 2pir^3/3, choose the one option closest to the radius of a hemisphere whose volume is 100cm^3. Options A. 0.28cm B. 3.63 cm C. 4.64cm D. 5.94cm E. 7.78cm F. 47.74cm
Interval of Convergence Functions
Find the interval of convergence of (a) f(x), (b) f'(x), (c) f''(x), (d) {f(x)dx En=1 [(-1)^n+1 (x-2)^n ] / 2
Power series centered at 0
Use the power series 1 / 1+x = En=0 (-1)^n x^n to determine the power series, centered at 0, for the function h(x) = x / x^2-1 = 1 / 2(1+x) - 1 / 2(1-x)
Taylor Polynomial Centered
Find the nth Taylor polynomial centered at c f(x)= (x)^1/3 n = 3 c = 8
Convergence or Divergence of P-Series Functions
Use theorem 8.11 to determine the convergence or divergence of the p-series En=1 3 / (n5/3)
Functions: Limits
Lim [1/(x-1) - 2/(x-1)] x→1
Differentiation: Word problem - rate of change
A water trough is 10 m long and a cross-section has the shape of an isosceles trapezoid that is 30cm wide at the bottom, 80 cm wide at the top, and has a height of 50 cm. If the trough is being filled with water at a rate of 0.2m3/min, how fast is the water level rising when the water is 30cm deep?
Rate of Change Word Problem
A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the dock that is 1m higher than the bow of the boat. If the rope is pulled in at a rate of 1m/s, how fast is the boat approaching the dock when it is 8m from the dock?
Volume of Revolution: Parabola and Lines
Find the volume of the solid generated by revolving the region between the parabola x = y^2 + 1 and the line x =3 about the line x =3.
Volume Calculation of a Cone: Changing radius at Constant Height
Derive a formula that estimates the change that occurs in the volume of a right circular cone when the radius changes from r0 to r1 and the height does not change.
Important information about Arc length
What is the arc length of the graph of function y=x (to the 2/3)-1 interval[0,4] ?
Length of Curve Functions
Length of curve interval [0,4] y= x (to the three halves) minus 1 y=x^3/2 - 1
Equation for tangent line in cartesian coordinates
Find equation of tangent line in cartesian coordinates. Give in polar coordinates: r=3-2costheta, at theta=pie divided by 3.
Arc length of graph of function for interval.
Arc length of the graph of function y=x (to the 2/3)-1 interval[0,4]
Calculating the length of a curve.
Find the length of the curve y=e^-x, 0<_x<_1
Proving that an equation is harmonic.
Prove that U(x,y)=e^(-x)[xsiny-ycosy] is harmonic.
Finding the limit of an expression.
Find the limit of following {1-cos(x)}/x^2 as x->infinity
Finding the maximum of a function.
Find the maximum of the following: f(x)=x^3-2x^2+1, -2<=x<=2
Using De Moivre's theorem.
If tan(A) = 1/2, find the value of tan(5A) Hint: Use De Moivre's theorem.
Differential Equation with a Natural Log
Find a general solution for this differential equation. Please see the attached file for the fully formatted problem. dy/dx + 2xy = xe^(-x2+2)
Differential Equation: System of Equations
For this problem state the method you used and show the work required to obtain the answer. Find the general solution for this system: this is a matrix x'= 3y+z y'= x+z+2y z"= 3y+x
Differential Equations
Hi, For this problem please state the method you used and show the work required to obtain the answer. Find the complete solution to this equation problem. y^3 - 2y^2 + y^1 = 2- 24e^(x) + 40e^(5x)