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calculus chapter 2

calculus chapter 2 - P if such a tangent line exists The...

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Chapter 2: Differentiation 2.1 Tangent Lines and Their Slopes -A tangent line to a circle meets the circle at one point, the circle lies on only side of the line, the tangent is perpendicular to the line joining the centre of the circle to the point of contact -tangent line: if Q is a point on C different from P, then the line through P and Q is a secant line to the curve -Nonvertical tangent lines lim f(xo + h) – f(xo) = m … then the right line having slope m and h->0 h passing through the point P = (xo, f(xo)) is called the tangent line to the graph of y=f(x) at P. equation of tangent line: y=m(x - xo) + yo -Vertical Tangents if lim f(xo + h) – f(xo) = (+/-) infinity, then the vertical line x=xo is h->0 h tangent to y=f(x) at P. If the limit fails to exist, y=f(x) has no tangent at P -The slope of a curve The slope of a curve C at a point P is the slope of the tangent line to C at
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Unformatted text preview: P if such a tangent line exists. The slope of the graph of y = f(x) at the point xo is… lim f(xo + h) – f(xo) h->0 h-Normals: If a curve C has a tangent line L at point P, then the straight line N through P perpendicular to L is the normal line slope of the normal = -1 ) slope of tangent 2.2 The Derivative -The derivative of a function f is another function f’ defined by f ‘(x) = lim f(x + h) – f(x) h->0 h at all points x for which the limit exists. If f ‘(x) exists, we say f is differentiable at x-equation of tangent line to y=f(x) at (xo, f(xo)) is y=f(xo) + f ‘ (xo)(x-xo)-value of the derivative of f at xo f ‘(xo) = lim f(xo + h) – f(xo) = lim f(x) – f(xo) h->0 h x->xo x-xo-if g(x) = c then g’(x)=0-if f(x) = x^r, then f ‘(x) = r x^(r-1)-a^n – b^n = (a-b)(a^(n-1) + a^(n-2)b + a^(n-3)b^2 + … ab^(n-2) + b^(n-1)-f ‘(absx) = x ) abs(x)...
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calculus chapter 2 - P if such a tangent line exists The...

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