Answers edited by sente

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• What is #int_0^pi (lnx)^2 / x^(1/2)#?
  
• How do you prove #sec^2 x - cot^2 ( pi/2-x) =1#?
  
• What is the Taylor series for #f(x)= cosx# centered on #x= pi/3#?
  
• How do you solve #log x + log (x-3) = 1#?
  
• How do you show that integration of #x^m e^(ax)dx = (x^m e^(ax) )/a - m/a int x^(m-1) e^(ax) dx#?
  
• How do you solve #sin^2 x - cos^2 x=0# for x in the interval [0,2pi)?
  
• Question #e07a4
  
• Question #d2752
  
• 6 equal circular discs placed so that their centres lie on the circumference of a given circle with radius (r), and each disc touches its 2 neighbours. What is the radius of a 7th disc placed in the centre which will touch each of the each existing ones?
  
• How do I find the natural log of a fraction?
  
• How do you solve #120=100(1+(.032/12))^(12t)#?
  
• How do you simplify #(sina+tana)/(1+cosa)#?
  
• How do you express #sqrt(-4/5)# as a product of a real number and i?
  
• How do I perform matrix multiplication?
  
• Question #c5432
  
• Question #6d8e6
  
• Determine the interval whereby 6x^2 + 44x + 70 ≥ 0?
  
• Question #9e52a
  
• How do you simplify # (x^(1/3) + x^(-1/3))^2#?
  
• What are the all the solutions between 0 and 2π for #sin2x-1=0#?
  
• What is #(-7pi)/8 # radians in degrees?
  
• How do you solve #tan^-1(2x)+tan^-1(x)= (3pi)/17#?
  
• How do you perform inversions for #y = x^2 and y = x^4?# Is #(dx)/(dy)# from the inverse #1/((dy)/(dx))?#
  
• What is the derivative of #f(x) = (lnx)^(x)#?
  
• How to write the first four terms of the Maclaurin series for the function f(x)=(x+1)e^(2x) given that ?
  
• If # n = 1/4#, what is the value of #(2n-5)/n#?
  
• Write the equation of a function with domain and range given, how to do that?
  
• How do I graph the ellipse with the equation #x^2+4y^2-4x+8y-60=0#?
  
• The movement of a certain glacier can be modelled by d(t) = 0.01t^2 + 0.5t, where d is the distance in metres, that a stake on the glacier has moved, relative to a fixed position, t days after the first measurement was made. Question?
  
• How do you solve #tan^2 x=tan x#?
  
• What's the LCM of 6 and 8?
  
• ?How do you find the sum of the infinite geometric series 0.03, 0.03, 0.003?
  
• How do you solve #2/(x+3)-4/(x^2+2x-3)=1/(1-x)#?
  
• How do you graph #g(x)= log_6 x#?
  
• How do you differentiate #p(y) = y^2sin^2(y)cos(y)# using the product rule?
  
• How do you use the ratio test to test the convergence of the series #∑(2k)!/k^(2k) # from n=1 to infinity?
  
• If the zeros of #x^5+4x+2# are #omega_1#, #omega_2#,.., #omega_5#, then what is #int 1/(x^5+4x+2) dx# ?
  
• How do you find the number of terms in the following geometric series: 100 + 99 + 98.01 + ... + 36.97?
  
• How do you verify #(cosX+sinX)/(cscX+secX) = (cosX)(sinX)#?
  
• How do you find all solutions to #x^5+243=0#?
  
• Find the matrix #A# for the linear transformation #T# relative to the bases #B = {1,x,x^2}# and #B' = {1,x,x^2,x^3}# such that #T(vecx) = Avecx#?
  
• How do you find the number of terms in the following geometric sequence: -409.6, 102.4, -25.6,..., 0.025?
  
• What is the distance between #(0, 0, 8) # and #(9, 2, 0) #?
  
• What is 0.09 (repeating) as a fraction?
  
• Question #0f6bd
  
• Question #a71e9
  
• A 45-45-90 triangle has a hypotenuse of length 14 units. What is the length of one of the legs?
  
• Question #9c5a0
  
• What is #lim_(x->0) (x^3+12x^2-5x)/(5x)# ?
  
• In the triangle embedded in the square what is the measure of angle, #theta#?
  
• What is the value of #1/n sum_{k=1}^n e^{k/n}# ?
  
• In 1/6=1.6666..., repeating 6 is called repeatend ( or reptend ) . I learn from https://en.wikipedia.org/wiki/Repeating_decimal, the reptend in the decimal form of 1/97 is a 96-digit string. Find fraction(s) having longer reptend string(s)?
  
• Question #de166
  
• Does #a_n=1/(n!) # converge?
  
• Find the area of the shaded region (green) knowing the side of square is #s = 25 cm#?
  
• How do you solve 2015 AP Calculus AB Question #1?
  
• Among all pairs of numbers with a sum of 101, how do you find the pairs whose product is maximum?
  
• Question #98d02
  
• How do you simplify #-2/(3-i)#?
  
• Question #a43bd
  
• Question #da791
  
• The center of a circle is at (0,0) and its radius is 5. Does the point (5,-2) lie on the circle?
  
• How do you convert #(3, -3sqrt3)# to polar form?
  
• Suppose that #lim_(xrarrc) f(x) = 0# and there exists a constant #K# such that #∣g(x)∣ ≤ K " for all " x nec# in some open interval containing c. Show that# lim_(x→c) (f(x)g(x)) = 0#?
  
• Question #5d611
  
• Is #sqrt(2)^(sqrt(2))# rational ? And #sqrt(2)^(sqrt(2)^sqrt(2))#?. And #sqrt(2)^(sqrt(2)^(sqrt(2)^cdots))#?
  
• What is the product of #2x^2+7x-10# and #x+5# in standard form?
  
• Is there a systematic way to determine the number of numbers between 10 and, say, 50, divisible by their units digits?
  
• What is the frequency of #f(theta)= sin 3 t - cos 21 t #?
  
• How do you integrate # 1/(1+e^x) # using partial fractions?
  
• Question #db818
  
• What is #1/3# of #18#?
  
• A composite geometrical shape is made up of a square, equilateral and right triangles. Calculate the area of hatched triangle?
  
• What are complex numbers?Thanx.
  
• Does this word construction (a meditation on Exodus 3) count as poetry, and if so how would you classify it?
  
• Solve for #x in RR# the equation #sqrt(x+3-4sqrt(x-1))+sqrt(x+8-6sqrt(x-1))=1# ?
  
• Suppose there are m Martians & n Earthlings at a peace conference. To ensure the Martians stay peaceful at the conference, we must make sure that no two Martians sit together, such that between any two Martians there is at least one Earthling?(see detail)
  
• How do you show that if #a+b=0#, then the slope of #x/a+y/b+c=0# is #1#?
  
• How do you simplify #((2n)!)/(n!)#?
  
• How do you use DeMoivre's Theorem to find #(1+i)^20# in standard form?
  
• How do you simplify # (2+2i)/(1+2i) # and write in a+bi form?
  
• What is 1 divided by 0.2?
  
• How do you simplify # cos (pi - theta)#?
  
• Question #b5ab2
  
• Is #sqrt33# an irrational number?
  
• Question #2b5bb
  
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