If limx→0 f(x) x2 = 2, evaluate the following limits. (a) limx→0 f(x) (b) limx→0 f(x) x Find the number a such that the limit exists. a = limx→−2 2x2 + ax + a + 6 x2 + x − 2 Find the value of the limit.
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If , evaluate the following limits.
(a)
(b)
Find the number such that the limit exists.
![(6 marks) A quadratic function f(x) = ax2 + bx + c can be represented by a vector [a b c]T in R3. Hence f(x) = 2x2 + x − 5 corresponds to the vector [2 1 −5]T while f(x) = 2x−1 corresponds to the vector [0 2 −1]T. (a) Find a matrix equation M[a b c] = z so that [a b c]T solves the equation exactly if f(x) = ax2 + bx + c satisfies f(1) = 2 and f′(0) = 3. (b) Which columns in M contain leading entries? How many parameters are there in the set of solutions for the equation? (c) Find a non-zero vector in the null space of the matrix.](https://www.doubtrix.com/uploads/editor/5737322387pCEZRoEbCB.jpeg)
