Questions asked by WolfyDude98

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• #y=tan^2(x)# Find #dy/dx#The answer is #2tan(x)sec^2(x)#. It was solved by substituting #u=tan(x)#. Now why did we not substitute #u=tan(x) for the second part? See below for more details
  
• #f(x)=-1/2x^2+6x-13#. The line #y=1/2x+c# is orthogonal to the graph of #f#. Then what is #c#?
  
• Why is #lim_(xrarr-3)(x^2-9)/(x+3)# #-6#? If I solve it by factoring, yes I get #-6# but I read somewhere that if the degree of the numerator is greater than the degree of the denominator, then the limit does not exist?
  
• Function f is given by #f(x) =x^2#. The graph of f is shifted vertically 3 up, and then scaled vertically by a factor 5. The result is the graph of the function #ax^2+bx+c# with a= 5 b= 0 And c =?
  
• Rewrite #sqrt((x^2*2^x)/((2x)^3*3^(2x)# as #a*x^b*c^x# for #x>0#?
  
• #f(x)=x^2#. The graph of #f# is shifted vertically #3# up, and then scaled vertically by a factor of #5#. The result is the graph of #ax^2+bx+c# where #a = 5, b= 0# and #c=# ?
  
• How do you differentiate #ln(6z^4+3z^2)#, #ln(6x^2+3z)#, and #ln(4z+1)# assuming #z>0#?
  
• #int_-2^1(x+1)(x-1)(x+2)dx#?
  
• #f(x)=4-x^2# We consider #A# to be the area of the region between #x=0# and #x=2# and #B# to be the area of the region between #x=2# and #x=p#.Find #p# such that #A=B#. Note that the area under the graph in this exercise is considered positive?.
  
• Bruce collects stamps. He has six times as many 10-cent stamps as 5-cent stamps, and he has some 20-cent stamps as well. Bruce has 72 stamps which are worth $8.40. How many of each stamp does he have?
  
• A light on the ground is 30 feet away from a building. A 4 foot man is walking from the light to the building at a rate of 3 feet per second and is casting a shadow on the building. At what rate is his shadow shrinking when he is 5 feet from the building?
  
• What mass of TiCl4 must react with an excess of water to produce 50.0 g of TiO2 if the reaction has a 78.9% yield? #TiCl_4 + 2H_2O → TiO_2 + 4HCl#
  
• What is the excess reagent and how many moles of it remain after 4.5 moles of sulphur react with 3.2 moles of ozone? #3S+2O_3→3SO_2#