Calculus Answers

Find two distinct points on the curve y=x³+x²-x+1 that have parallel tangent lines

identify a mathematician that contributed to the development of theory of functions in mathematics. state the contribution made and why was it so important to the field of mathematics

State the domain and range of the relations described.

y = x-1, x ≠ 2

= 1 , x = 2

Question 3 Verify using the definition of limit (with ϵ and δ) that lim x→1 (1/2 |x − 1| + 3) = 3, explain all the steps and the overall significance of what you do. [16]

From the graph of f given in the picture below, sketch all the steps to draw the graph of 1/2 f(2x + 2) − 2 

 If a third degree polynomial has a lone x-intercept at

x = a , discuss what this implies about the

linear and quadratic factors of that polynomial.

Consider the surface S = n (x, y, z) | z = p x 2 + y 2 and 1 ≤ z ≤ 3 o .(a) Sketch the surface S in R 3 . Also show its XY-projection on your sketch. (2) (b) Evaluate the area of S, using a surface integral

Expand each of the following functions in a Fourier sine series then a Fourier cosine series on the prescribed interval.

(i) 𝑓(𝑥) = 𝑒^−𝑥 ; 0 < 𝑥 < 1,

(ii) 𝑓(𝑥) = { 𝑥 0 < 𝑥 < 𝑙/2 𝑙 − 𝑥 𝑙/2 < 𝑥 < 𝑙 ; 0 < 𝑥 < 𝑙,