Answers created by Steve M

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• Given `int e^x(tanx + 1 )secx dx = e^xf(x)+C`.Write f(x)satisfying above.How can you solve it ?
  
• If d^(2)x/dt^(2)+g/b(x-a)=0,(a,b,g being positive constants) and x=a' and dx/dt=0 when t=0,show that x=a+(a'-a)cos{√(g)/(b)t}?
  
• If `lim_(x rarr 2) (ax^2-b)/(x-2)=4` then find the value of a and b?
  
• How do you graph `y=1+5cos(x-pi)`?
  
• How to use u substitution for `sin2x`?
  
• Identify the following differential equation and hence solve it `y'=-4/x^(2)-y/x+y^(2)` ?
  
• What is meant by the determinant of a matrix?
  
• How do you graph `y = 1/sin x`?
  
• Thoughts on the recent announcement made about the future of the Socratic website? Share them here!
  
• If f is a continuous function such that `int_0^xf(t)dt=xe^(2x)`+ `int_0^xe^-tf(t)dt` for all x, find an explicit formula for f(x) ?
  
• How do you integrate `int dx/sqrt(x^2-64)` using trig substitutions?
  
• Given that y=2 when x=-3,What is the value of y when x=5 for the differential equation y dy/dx =2x+3?
  
• If `A= <2 ,-3 ,9 >` and `B= <0 , 3, 7 >`, what is `A*B -||A|| ||B||`?
  
• What is the formula for the sum of an arithmetic sequence?
  
• How do I find out values of stuff like "sec(pi/3)" without a calculator?
  
• Let g(x)=`int_0^xf(t)dt` where `f` is the function whose graph is shown. Evaluate g(0), g(2), g(4), g(6) and g(12)?
  
• How to prove newton's method?
  
• Solve the following differential equation? `(2x+y+3)dy/dx=x+2y+1`
  
• How do you use double angle formulas to calculate cos 2x and sin 2x without finding x if `cos x = 3/5` and x is in the first quadrant?
  
• How do you use the Trapezoidal Rule to approximate integral `int(2/x) dx` for n=4 from [1,3]?
  
• How do you graph `y < x^2- 5x`?
  
• Let `f` and `g` be two real-valued functions such that `f(x+y) + f(x-y) = 2f(x).g(y) AA x,y in R`. If `f(x)` is not identically zero and `|f(x)| <=1 AA x in R`, then prove that `|g(y)| <=1 AA y in R`?
  
• `A/B=B/A" "` is true if?
  
• `f(x-y)=f(x)/f(y)` and `f^'(0)=p,f^'(a)=q` then what is `f^'(-a)?`
  
• `int_0^1 lnx/(1+x)dx` ?
  
• Given `f(x)=3x^2+4x-5` and `g(x)=2x+9`, how do you find `f(x)+g(x)`, `f(x)-g(x)` and `f(x)*g(x)` and `(f/g)(x)`?
  
• Integrate `\int {sin(2x)}/{sinx}dx` ?
  
• Solve the differential equation `y'=(y-x)^2`?
  
• How did newton discover the law of universal gravitation?
  
• Find `tan theta` if `sec theta = 17^2` ?
  
• If a circle has center (0,0) and a point on the circle (-2,-4) write the equation of the circle.?
  
• How to differentiate `y=xe^x(sinx+cosx)` ?
  
• What is the square root(80) over square root(50)?
  
• If y = f(x)g(x), then dy/dx = f‘(x)g‘(x). If it is true, explain your answer. If false, provide a counterexample. True or False?
  
• What is the derivative of `f(x) = e^(x^2 + lnx^3)`?
  
• If , `y=sqrt(x/a)-sqrt(a/x)` So, Prove that ?? `2xy(dy/dx)= x/a-a/x`
  
• If y=at^2 and x=2at where x,y,t are variables and is a constant then find dy/dx ?
  
• How do I solve the formula `16t^2 - vt - 40 = 0` for `t`?
  
• Given `f(x)=1/8x-3` and `g(x)=x^3`, how do you find `(f^-1of^-1)(6)`?
  
• What will be the Evaluate the following integrals ? (1) ∫ (a/x^2 + b/x) dx (2) ∫ (3x^-7+x^-1) (3) ∫ (√x+1/√x)^2 dx
  
• If `A= <-5 ,3 ,-3 >` and `B= <2 ,2 ,-7 >`, what is `A*B -||A|| ||B||`?
  
• How do you differentiate `y = (ln(x^2))^(2x+3)`?
  
• Let f(x,y)=xe^y -ye^x The gradient of f at (0,0) is ∇f(0,0)=?
  
• How do you solve `x+3y=6`, `4x-5y=7` by graphing?
  
• How do you multiply `(a+b)(a+b)(a+b)`?
  
• How do you prove that csch^-1(x) = sinh^-1(1/x)?
  
• The polynomial `8x^3-36x^2+22x+21=0` has roots which form an arithmetic progression. How do you find the roots?
  
• What is the derivative of `arctan (1/x)`?
  
• Prove that product of two parts of a constant number will be maximum when both parts are equal?
  
• How do you differentiate `f(x)=sin(x)` from first principles?
  
• Prove that tan(π/4+A)tan(3π/4+A)=-1?
  
• How do I solve `log_2 5x+4=y?`
  
• If x<0and y<0 x+y+x÷y=1÷2 and (x+y)x÷y=-1÷2 then find x and y?
  
• Are there multiple answers to integrals?
  
• How do you integrate `int 1/sqrt(-e^(2x)-20e^x-136)dx` using trigonometric substitution?
  
• How does `1+2+3+...+(n-1)=1/2(n)(n-1)`?
  
• Would like to solve this integral but it kind of messy especially when it comes to end?
  
• Find `\int_0^ooe^(-ax)\sin(bx)dx`?
  
• How to prove 5secx+4 =9secsquarex- 4tansquarex?
  
• Solve the differential equation by using CF and PI : `(D^2-D-2)y=cos 2x` ?
  
• Differentiate y=x^2+bx+c, and hence find b and c if: the parabola has y-intercept and has gradient -2 there?
  
• How would the trigonometric expression sin[(arccos (0)-arcsin(x)]be written as an algebraic expression?
  
• Algebraically determine the exact value of?
  
• Separable Differential Equation with Initial Value?
  
• Is there an algebraic formula to find out the area of a hexagon?
  
• What are three fractions that can be written as percentage between 50% and 75%?
  
• Solve integral `\intx^p/(x\sqrt(1-x^2))dx`?
  
• Find derivatives y=tanh sqrt 1+t^2 ?
  
• How would you find the center and radius of `x^2 + y^2 + 12x - 6y = 0`?
  
• How do you solve `5^x=52`?
  
• What is the common difference? if an A. P has the sum of first and last term is 43 and the third is 11 the sum is 258
  
• How do you identity if the equation `25y^2+9x^2-50y-54x=119` is a parabola, circle, ellipse, or hyperbola and how do you graph it?
  
• A piece of wire 11 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. How much wire should be used for the square in order to maximize and minimize the total area?
  
• Let `siny + cosx = 1` then find `(d^2y)/(dx^2)`?
  
• INTEGRATION arctanx ?
  
• Find the area of the region inside these curves?
  
• How do I know which Newton's law to use in any question?
  
• Did I do this First order linear differential equation right?
  
• If `f={(-3,4),(-1,5),(-2,6),(2,4),(0,3)} and g={(4,3),(5,7),(3,0),(6,0)}` then find set of ordered pair of gof and fog and represent in arrow diagram.?
  
• What is the net area between `f(x) = 4/x` and the x-axis over `x in [1, 2 ]`?
  
• How do you integrate `int 1/sqrt(e^(2x)-2e^x+2)dx` using trigonometric substitution?
  
• Find the limit by evaluating the derivative of a suitable function at an appropriate point? lim t approaches 0 (1-(1+t)^2/t(1+t)^2) Thank you very much
  
• How to show the following are true for the two vectors 𝑢̅=4𝑥𝑦𝑖̅−2𝑧𝑗̅+(11𝑥^3)𝑘̅ ⁡and 𝑣̅=(𝑥𝑦/𝑧)𝑖̅+(3𝑥^2)𝑗̅ +6𝑘̅ ? a. ∇×(𝑢̅+𝑣̅)=∇×𝑢̅+∇×𝑣̅ b. ∇.(𝑢̅+𝑣̅)=∇.𝑢̅+∇.𝑣
  
• The first four terms in binomial expansion of (a+b)ⁿ , in descensing power of a , are w,x, y and z respectively.Show that (n-2)=3nwz?
  
• Is it possible to solve this integral by hand or by conventional methods?
  
• Find the partial sum?
  
• How to solve this first order linear differential equation?
  
• How do you find the vertex of a quadratic equation?
  
• 2nC3:nC2=44:3? Permutation And book answer is 6
  
• What is the general solution of the differential equation? : `y''+4y=2sin2x`
  
• Let f:Rise defined from R to R . find the solution of f(x) =f^-1 (x)?
  
• How to evaluate the triple integral with step by step solution please?
  
• `x^3+i =0` Find all complex number solutions. Write in trigonometric form. I know I need to find r and the angle. Need help with the steps?
  
• What is the differential equation?
  
• The curves C1 and C2 are defined by the following parametric equations: C1: x=1+2t, y=2+3t, 2<t<5 C2: x=1/(2t-3), y=t/(2t-3), 2<t<3 Show that both curves are segments of the same straight line???
  
• How to solve?(sin45+cos60)/(sin60+tan30) Step by step
  
• `lim_(x->0)sin(1/x)/(sin(1/x))` ?
  
• When using integration to find an area, exactly which "area" is found?
  
• How do you integrate `int 1/sqrt(e^(2x)+12e^x+40)dx` using trigonometric substitution?
  
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