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The phrase "a and b are roots of 2x^2+6x+7" is just a way of saying that x=a and x=b solve the equation 2x^2+6x+7=0. Check out that by diving by 2 on both sides of this equation we get that that...
They have multiplied the fractions correctly but they are still incorrect. The student has assumed that a bag with 60% green beads contains 10 beads. If the bag had 100 beads and 60 were green, 60% of the...
Recall the product rule for differentiation. If y=uv, where u and v are functions defined by functions of x, then we can take the derivative of y as: y'=u'v+v'u () (where ' denotes the derivative) ...
Step 1:Replace any obvious in the integral with the substitution u=x+2 ∫_(-1)^1 3/√u dx
Step 2: Differentiate the substitution u=x+2 to find an expression for dx (to differentiate multiply by the p...
First, we use the trig identities: cos2x=cos^2x-sin^2x, cos^2x+sin^2x=1 and sin2x=2sinxcosx to transform the integral to ∫(cos2x)/(1+sin2x)dx.We know that ∫f'(x)/f(x)dx = ln|f(x)|+c, so we let f(x)=...
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