Answers created by Noah G

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• Use taylor series to evaluate `f^11 (0)` for `f(x) = x^3 cos(x^2)` ?
  
• Establish the identity. ln |cot u| = ln |cos u| - ln |sin u| ____________________ Could someone please explain to me how to solve this?
  
• How To sketch the graph of C and label relevant points?
  
• The sequence a1, a2, a3... an is an arithmetic sequence. a4=-a6. What is a5?
  
• Convert into standard form and sketch this Quadric surface equation : ?
  
• What is the general equation for the arclength of a line?
  
• Integrate `int xe^(2x)dx` ?
  
• What is the arclength of `f(x)=sqrt(4-x^2)` in the interval `[-2,2]`?
  
• Can you solve a question that gives you two side lengths of a right angled triangle without Pythagorean Theorem?
  
• Help with calc please?
  
• How do you find the slope of the curve `y^3-xy^2=4` at the point where y=2?
  
• Determine x so that x, 1/2x+7, and 3x-1 are the first three terms of an arithmethic sequence?
  
• Who's interested in a new Socratic on a different website?
  
• When will the slope field for the differential equation `(2x)/(4y-xy)` have vertical segments?
  
• A piece of wire 10 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. How should the wire be cut so that the total area enclosed is maximum?
  
• The taylor series about 0 for the function f(x)=1/1-x ?
  
• Function f(x)=(x^3)(e^x) is strictly increasing on the interval of?
  
• Suppode f(x)=cx^2+2x,if x<2.and 2x+4,if x>=2. f(x) is continuous on(-∞,∞).Then the value of c is?
  
• How to simplify `cos^2 2theta-sin^2 2theta`?
  
• What is the answer of 1-cot²a=?
  
• How do you solve `e^(2x)-(4e^x)+3=0`?
  
• A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola `y=6-x^2`. What are the dimensions of such a rectangle with the greatest possible area? thanks for any help!?
  
• Which of the following has larger size and why? 1) Be or Mg 2) Li or Na
  
• How do I determine if the improper integrals converge or not?
  
• How do you know when to use L'hospital's rule twice?
  
• A particle is travelling an elliptical path described by `(3sin(2t)), 4cos(2t))`. Find the points at which it is travelling fastest?
  
• Ap Physics C 1991 Question 1?
  
• Can I get help with this graph? It involves derivatives and differentiation. I got h'(2) right but need help with h'(1) and h'(3)
  
• How do you find the average value of the function for `f(x)=x+sinx, 0<=x<=2pi`?
  
• Ap Physics C 1995 Question 1?
  
• Ap Physics C 2002 M2?
  
• Ap Physics C 1989 M2?
  
• 8. The slope of the curve y=x³-3x+1; - infinity < x <infinity is minimum at: A. X= - 1 B. X= 1 C. X=0 D. X= +1,-1 Ans. C Please give explanation???
  
• The volume of cube is 216 cm cube. If the length of the edge is increased by two times, what should the volume of new cube?
  
• The diagram shows two curves with equations y=sin x and y=sin2x for x values between 0 and pi. the curves meet at the origin and at the points P and Q. a) find P and Q? b)find the areas of the shaded regions A1 and A2?
  
• How do you prove `Tan x+Cot x =Sec x Csc x`?
  
• Prove: is y = tan(2x), than y" = 4y . y' ? Thank you!t
  
• Given the set: `{9,0,6,-10,2,x,3}`, for what x would the mean of the set be -2?
  
• Given sin 40° ≈ 0.64, cos 40° ≈ 0.77, sin 15° ≈ 0.26, and cos 15° ≈ 0.97, which expression could be used to estimate sin 55°?
  
• If `h^2+k^2=23hk`, where h>0, k>0, show that log `(h+k)/5=1/2 (logh+logk)`?
  
• A satellite X of mass m orbits the Earth with a period T. What will be the orbital period of satellite Y of mass 2m occupying the same orbit as X?
  
• How do you write the expression `cos25^circcos15^circ-sin25^circsin15^circ` as a sine, cosine or tangent of an angle?
  
• If `f(x/(x+1))=(x-1)^2`, what is `f(3)`?
  
• How can this be done? Finding the radius of convergence and the interval of convergence of the series?
  
• Help please??
  
• The sum to infinity if a GP is 16 and the sum of the first 4 terms is 15. Find the first four terms?
  
• Determine the Maclaurin series representation for f(x)=e^x/x ?
  
• What's the difference between radius of convergence and interval of convergence?
  
• Out of curiousity, what type of function would this be?
  
• How do you solve `e^ { 3c - 2} = b`?
  
• Express the following as a function of a single angle? Cos^2(81 deg) - sin^2(81 deg)
  
• How do you show that the series `ln1+ln2+ln3+...+lnn+...` diverges?
  
• How do you solve these integrals? help please!
  
• What does the graph of g(x) look like given that `f(x)=(d/(dx))g(x)` and `g(0)=0`?
  
• Find the area of a single loop in curve `r=\sin(6\theta)`?
  
• Can you evaluate the integral by interpreting it in terms of areas?
  
• What is the difference between an ether and an ester?
  
• How do you solve `Cos(2x)cos(x)-sin(2x)sin(x)=0`?
  
• How to fine the equation of the curve ?
  
• Find a curve through the region in the XY-plane whose length from X=0 to X=1 is L=INTEGRATION sqrt 1+1/4e^xdx?
  
• F(x)=root of (x^2+16) and (f(k))^2=20,k>0.what is the value of f(k+1)?
  
• Find the slope at any value of x,if y=(x)^lnx?
  
• `2tan^-1(x)+sin^-1((2x)/(1+x^2))` is independent of `x`, then?
  
• What is the equation of the parabola that has a vertex at `(0, 16)` and passes through point `(2,20)`?
  
• Find all numbers C that satisfy the conclusion of the MVT of f(x) = Xln(x) [1,2] ?
  
• How to integrate #int(e^2x+e^-2x)/(e^2x-e^-2x)dx?
  
• Please show the integration of `(x^3)/((x^4+7)^8)dx` step by step?
  
• How to find the general solution of `x dy/dx = xy + y` ?
  
• How do you find the y ? ln(y^2-1) - ln(y+1)=ln(sinx).
  
• A triangular playground has angles with measures in the ratio 7 : 3 : 5. What is the measure of the smallest angle?
  
• A particle moves in a straight line so that at time t its displacement from a fixed origin is x and its velocity is v. If its acceleration is 4 + x and v = 1 when x = 0, what is v when x = 1?
  
• For a continuous function `f`, is it generally true that `\int_0^2 f(x)dx = \int_0^1 f(2x)dx`?
  
• Find x where 0<=x<=2pi sin x - cot^2 x = 1 Anyone know how to do these things??
  
• When the expression `2x^3 + ax^2 -5x -2` is divided by `2x-1`, the remainder is `-3.5` . Determine the value of the constant `a`. Can someone please help?
  
• Can someone please help with this **logarithms** question?
  
• What is the limit of `x^(1-x)` as x approaches 1? The hint is "Use the properties of logarithms to simplify the limit". But I just can think in the straight answer 1, by substitution. Can someone develop in steps using this hint, please?
  
• 1 The sum of the three smallest positive values of theta such that 4(cos*theta)(sin*theta) = 1 is k*pi. Find k?
  
• Power series?
  
• When will the slope field for the differential equation `dy/dx=(yx^2+xy^2)/(3x+y)` have horizontal segments?
  
• How do you find the volume of the solid obtained by rotating the curve about the y-axis over [0,1]?
  
• Find the point on the curve y=cosx closest to the point (0,0)?
  
• How do you verify `sinx/(1-cosx) - (sinxcosx)/(1+cosx)=cscx(1+cos^2x)`?
  
• How to differentiate ln`x/2` and ln(`√(1-`1/x`)`) respect to x?
  
• For `g(x)=x^(3) +2x^(2) +cx +k` (c and k are real numbers) : a. If g has exactly one stationary point find the value of c. b. If the stationary point occurs at a point of intersection of `y=g(x) and y=g^(-1) (x)`, find the values of k?
  
• Find the interval and radius of convergence of the following power series (problem #1a)?
  
• Given that `xe^y = x+1`, show that `e^y + xe^ydy/dx = 1`?
  
• Use series to evaluate the limit `\lim_(x\rarr0)(x^2/2-1-\cos(x))/x^4`?
  
• How do you use `f(x) = sin(x^2-2)` to evaluate `(f(3.0002)-f(3))/0.0002`?
  
• What the area of the figure bounded by the given curve y=(x*(sqrt36-x^2)) (0_< x_< 6)?
  
• If the normal to the curve `y=xlnx` is parrallel to the straight line `2x-2y+3=0` ,then the normal equation is...... a.`x-y=3e^-2` b.`x-y=6e^-2` c.`x-y=3e^2` ?
  
• Cot x/ tan x × sec²x = cosec x how? prove it
  
• How do you draw slope fields?
  
• Help with Calculus?
  
• Please Evaluate the problem?
  
• If 0< a_n <b_n and the series a_n diverges then the series b_n diverges. Is this statement true or false?
  
• How do I solve log_3(2x-1)≤2 for x?
  
• A box in the shape of a rectangular prism has a volume of `6x^3+27x^2-15x`. What are the dimensions of the box?
  
• Evaluate this integral of ydy/√y+1 using substitution method?
  
• If `e^x+e^y=e^(xy)` Then, dy/dx=?
  
• What are two positive numbers whose sum of the first number squared and the second number is 54 and the product is a maximum?
  
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