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Since F'(0)=1 (that is, the graph of F is tangent to the diagonal at x=0) this fixed point must be neutral. Moreover, graphical analysis suggest that the fixed ... So we get vertical asymptotes at x = π/2 and at x = 3π/2 in the graph of tangent function. Let us plot the x-axis with the angles from 0 to 2π with ... ... tangent is π. y = tan x. A graph of y = cot x is given in figure 3. Notice there are asymptotes for angles where cotangent is undefined, such as x = 0 and x = π ... tan x − (3x2 − 5x).(tan x)′. (tan x)2. = (6x − 5). tan x − (3x2 ... (c) f is not differentialble at x = 0,x = 4 . Page 4. Page 5. 9. x2y = 13, 500 ... ... x) = 0, d(x, y) = 1 for any x, y ∈ X, x 6= y. 2. To show that Td ⊂ Tρ, we ... = |(tan x − tan z) + (tan z − tan y)|. ≤ |(tan x − tan z)| + |(tan z ... Find the equation of the tangent to the curve x = cos(2y+) at 0, π. Give. 1 (0.4). your answer in the form y = ax + b, where a and b are constants to be found. This is the same as x < tan x. (b) Show that x/ sin x is a strictly increasing function on (0, π/2). Solution: If ... The function has a discontinuity at x = 0 because it is not defined at x = 0. ... 1 Based on the graph, why do you think y = tan(x) is said to have an infinite ... Task. The function f(x) = x − tanx has a simple root near x = 4.5. Use one ... y = x y = tan x. 0 π/2 π. 3π/2 x. From the graph it can be seen that the ... x1=x0-f(x0)f′(x0) ... 4. sin(x), sin(x). 5. cos(x), cos(x). 6. tan(x), tan(x). 7. sec(x), sec(x). 8. cosec(x), csc(x). 9. cot(x), cot(x). 10. sin- ...