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Suppose that x = x (t ) and y = y (t ) and differentiate the following equation with respect to t. Solution x 3 y 6 + e 1- x - cos (5
Product Rule If the two functions f(x) & g(x) are differentiable (i.e. the derivative exist) then the product is differentiable and,
Steps for Alternating Series Test Suppose that we have a series ∑a n and either a n = (-1) n b n or a n = (-1) n+1 b n where b n > 0 for all n. Then if, 1.
A triangle has vertices A (-1, 3, 4) B (3, -1, 1) and C (5, 1, 1). The area of ABC is a) 30.1 b) 82.1 c) 9.1 d) 52.1
Graph f ( x ) = e x and g ( x ) = e - x . Solution There actually isn't a lot to this problem other than ensuring that both of these exponentials are graphed somewhere.
The m&m factory produces 2,500 packs of plain m&ms each day. Represent the total number of packs of plain m&ms the factory makes each day
Critical point of exponential functions and trig functions, Let's see some examples that don't just involve powers of x. Example: find out all the critical points for the
find any integer from 1-128 on a logarithmic scale
Let R be the relation on S = {1, 3, 6, 9, 27} defined by aRb iff a|b. (a) Write down the matrix of R. (b) Draw the digraph of R. (c) Explain whether R is reflexive, irrere
(a) Find an example of groups G, H, K with K H and H G but K G. (b) A subgroup H of G is characteristic if σ(H) ⊆ H for every group automorphism σ of G. Show that eve
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