Questions asked by Sarah

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• How do I solve #(cot(x)+tan(x)) / (csc(-x))#?
  
• Use a double-angle or half-angle formula to simplify the given expressions: 1. If cos^2(39degrees)-sin^2(39degrees) = cosA then what does A equal? 2. If cos^2(3x)-sin^2(3x) = cosB, what does B equal?
  
• If sin^4x = A + Bcos2x +Ccos4x, then what is A, B, and C equal to?
  
• If x+2=4sinx for 0<x<(pi/2), express cos(2x) in terms of x. Cos(2x)=?
  
• Reduce to one trig identity. sec(x)+sin(x)tan(-x)=? I know it equals cos(x) but how?
  
• How do you derive the trigonometric sum and difference formulas for sin, cos, and tan? I.e: How do I derive something like sin(x+y)=sinxcosy+cosxsiny?
  
• How do you derive the trigonometric formulas for double and half angels for sin, cos, and tan? I.e: How do I derive something like sin(2x)=2(sinx)(cosx)?
  
• How do I find the exact value of cos(2sin^-1(12/13))?
  
• How do I rewrite the following two trig expressions with exponents no greater than 1? Such as (A) (Sin^3)x (B) (cos^4)x?
  
• How do I find all the solutions for cos(x)tan(x)=tan(x) on one interval rotation of the unit circle?
  
• Solve the following equation in the interval [0, 2pi]. 2(sin(t))^2-sin(t)-1=0?
  
• Let u = <-3, 2>, v = <3, 0>, and w = <5, 2>. Find the vector x that satisfies 8u-v+x=3x+w. In this case, vector x is?
  
• How do you find the angle in radians between the vectors a = <sqrt(3), -1> and b = <0, 3>?
  
• Consider the three points: A=(9, 8), B=(7, 10), C=(10, 6). What is the angle between AB and AC?
  
• A triangle is defined by the three points: a=(7, 10), b=(9, 10), and c= (5, 6). How do I determine all three angles in the triangle (in radians)?
  
• ||v|| = 4. ||w|| = 4. The angle between v and w is 2.1 radians. Given this information, calculate ||4v+2w|| and ||1v-3w||?
  
• How would I find the limits of the function below?
  
• How do you find the limits of the function below?
  
• How do I find the #lim_(x to 6) (5x)/(3+x^8)#?
  
• Considering the reaction shown below, how much thermal energy would be required to run the reaction with 5.0 g of hydrogen and 25 g of iodine?
  
• How do I simplify 7/(7+5i)? (Hint: The irrational number i equals 1 when i^2.)
  
• How do I identify the symmetry of the graph #(3x^2)+(3y^2)=5#?
  
• How do I describe the end behavior without graphing of f(x)=1-2x^2-3x?
  
• How do you factor x^3+9x^2+24x+16 if you know that x+4 is a factor?
  
• How do I find the domain and (if any) discontinuities for #g(x)=(x^2+6x+9)/(x+3)#? I don’t entirely understand what is being asked by domain and discontinuity.
  
• How do I find the horizontal, vertical, and oblique asymptotes (If any exist) for f(x)=5x^3+49x^2+127x+75/(x^2+9x+18)?
  
• How do I determine the end behavior of the graph, f(x)=(3x-3)/(4x+5), in limit notation?
  
• How do I expand In(m^2n^3)/(sqrt(p))?
  
• What is the standard entropy of the reaction below at 25 degrees Celsius? H2O(g) + C (graphite, s) --> H2(g) + CO(g)
  
• The elementary reaction 2H2O(l) <--> 2H2(g) + O2 (g) has the partial pressures of H2O, H2, and O2 reach 0.0500 atm, 0.00200 atm, and 0.00450 atm respectively. What is the value of the equilibrium constant at this temperature?
  
• How do I calculate Kp for C+CO2=2CO given the following reactions? C+2H2O=CO2+2H2 and H2+CO2=H2O+CO.
  
• How do I calculate mass loss per mm^2 given length, diameter, initial and final mass values?
  
• How do I find the horizontal limits of f(x)=(2x^3-11x^2-11x)/(5-9x-6x^3)?
  
• How do I find this in terms of constant A? lim as h--> 0 7(a+h)^2-7a^2.
  
• How do I find the equation of the tangent line to the curve at the given point, (2, -4)? y=4x-3x^2.
  
• How do I solve this? A generic salt, AB3, has a molar mass of 297 g/mol and a solubility of 7.30 g/L at 25 °C. What is the Ksp of this salt at 25 °C? AB3(s) <--> A^(3+) + 3B^(-)
  
• How do I find the molar solubility of this compound? The Ksp of cerium (III) iodate, Ce(IO3)3, is 1.40 × 10-11.
  
• Silver chromate is sparingly soluble in aqueous solutions. The Ksp of Ag2CrO4 is 1.12× 10^–12. What is the solubility (in mol/L) of silver chromate in 1.50 M potassium chromate aq solution? In 1.50 M silver nitrate aq solution? In pure water?
  
• What concentration of #"SO"_3^(2–)# is in equilibrium with #"Ag"_2"SO"_3(s)# and #1.80 * 10^-3# #"M"# #"Ag"^(+)# ? The #K_(sp)# of #"Ag"_2"SO"_3# is #1.50 * 10^–14#
  
• How do I find f'(x) of f(t)=9/(t^3)?
  
• How do I solve f'(x) for 3sqrt(t)+(11/sqrt(t))?
  
• How do I solve f(x)=((5x^2)+(2x)+2)/(sqrt(x)) for f'(x)?
  
• How do I find f'(x) for f(x)=7(x^(4/5))-8(x^(6/7))?
  
• How do I solve f'(x) for f(x)=7(x^2)+(2/(x^2))?
  
• How do I find the equation of the tangent line to the curve y=2xcos(x) at the point (pi, -2pi)? The equation of this tangent line can be written in the form y=mx+b where m and b are?
  
• If f(x)=5x(sinx)(cosx), then what does f'(x) equal?
  
• How do you differentiate y=(2+sinx)/(x+cosx)?
  
• If f(x)=(4x+5)/(5x+6), how do you find f'(x)?
  
• How do I find an equation for the tangent line to the graph of #f(x)=(sqrt(x))/(4x-8)# at the point #(3, f(3)#)?
  
• How do I use logarithmic differentiation to determine the derivative for #f(x)=((x^5)((x-7)^5))/(x^2+2)^8#?
  
• If f(x)=(4x^2tan(x))/(sec(x), how do I find f'(x) and f'(3)?
  
• How do I find the derivative of k(a)=sin^5acos^4a?
  
• Consider the function 1-7x^2 on the interval [-2, 7]. How do I find the average slope on this interval? Find the one point in which f'(c) is equal to the mean slope.
  
• If #f(x)=(x+3)(x-1)^2#, how do you find the local maxima and minima at #x# using the second derivative?