1. Find dy/dx given y = f(x) 2. a. Find dy/dx using implicit differentiation given an...

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1. Find dy/dx given y = f(x) 2. a. Find dy/dx using implicit differentiation given an the equation f(x, y) = 0 b. Find the tangent line to the graph of f(x, y) = 0 at a given point 3. Given that x, y and z are functions in t, find dx / dt in terms of x, y, z, dy/dt and dz/dt 4. a. Draw a curve y = f(x) given the sign-chart of its derivative y': b. Draw a curve y = f(x) given the sign-chart of its 2nd derivative of y": 5. Use derivatives to find approximate changes in geometric measurements. For all the formulas below, be able to find the differential of one variable with respect to another variable and find the rate of changes at given specified values. Perimeter and Area of Plane Figures Triangle Volume and Surface Area of Solid Figures Rectangular Prism 5=2w+2+2 Rectangle A-w Parallelogram P=20+2b A-M Trapezoid Pm Circle C=2xr Am 40040 Right Circular Cylinder Var Sphere Right Circular Cone For the circle and sphere 1. a. Find dC in term of dr. What is dC if dr = 1cm? b. Express the radius r in terms of the circumference C. Find dr in terms of dc. Find dr if dC = 2 cm. Ans: a. dC = 2dr, dC = 27 cm if dr = 1 cm b. r = C/(2x), dr=dC/(2n), dr = 1/ cm 2. a. Find dA in term of dr. What is dA if when r = 12 cm and dr = 0.1 cm? b. Express the radius r in terms of the area A. Find dr in terms of dA. Find drif A 16 cm and that dA-1 cm. 3. a. Find area A in terms of the circumference C. Find dA in term of dC. What is dA if when C-8x cm and dC = 0.1 cm? b. Find the circumference C in terms of the area A. Find dC in terms of dA. Find dC if A 16x cm and that dA-1 cm. Ans: a. A=C/(4x), dA = C/(2n) dC, dA = 0.4 cm b. C=22A12, dC = AdA, dC = 14 cm 1. a. Find dV in term of dr. What is dV if dr = 0.1cm when r = 10 cm? b. Express the radius r in terms of the volume V. Find dr in terms of dV. Find dr if dV 1 cm when V = 36 cm. = Ans: b.r-v, dr-v dv. dr (2) 36 0.190. = 2. a. Find dS in term of dr. What is dS if dr = 0.1cm when r = 10 cm? b. Express the radius r in terms of the surface area S. Find dr in terms of dS. Find dS if dV 1 cm when V = 36 cm. Ans: a. dS=8xr dr, ds = 8 cm 3. a. Find volume V in terms of the surface S. Find dV in term of dS. What is dV if when S = 16x cm and that dS = 1 cm? b. Find the surface S in terms of the volume V. Find dS in terms of dV. Find dS if V = 36 cm and that dV = cm. 2 1. Find dy/dx given y = f(x) 2. a. Find dy/dx using implicit differentiation given an the equation f(x, y) = 0 b. Find the tangent line to the graph of f(x, y) = 0 at a given point 3. Given that x, y and z are functions in t, find dx / dt in terms of x, y, z, dy/dt and dz/dt 4. a. Draw a curve y = f(x) given the sign-chart of its derivative y': b. Draw a curve y = f(x) given the sign-chart of its 2nd derivative of y": 5. Use derivatives to find approximate changes in geometric measurements. For all the formulas below, be able to find the differential of one variable with respect to another variable and find the rate of changes at given specified values. Perimeter and Area of Plane Figures Triangle Volume and Surface Area of Solid Figures Rectangular Prism 5=2w+2+2 Rectangle A-w Parallelogram P=20+2b A-M Trapezoid Pm Circle C=2xr Am 40040 Right Circular Cylinder Var Sphere Right Circular Cone For the circle and sphere 1. a. Find dC in term of dr. What is dC if dr = 1cm? b. Express the radius r in terms of the circumference C. Find dr in terms of dc. Find dr if dC = 2 cm. Ans: a. dC = 2dr, dC = 27 cm if dr = 1 cm b. r = C/(2x), dr=dC/(2n), dr = 1/ cm 2. a. Find dA in term of dr. What is dA if when r = 12 cm and dr = 0.1 cm? b. Express the radius r in terms of the area A. Find dr in terms of dA. Find drif A 16 cm and that dA-1 cm. 3. a. Find area A in terms of the circumference C. Find dA in term of dC. What is dA if when C-8x cm and dC = 0.1 cm? b. Find the circumference C in terms of the area A. Find dC in terms of dA. Find dC if A 16x cm and that dA-1 cm. Ans: a. A=C/(4x), dA = C/(2n) dC, dA = 0.4 cm b. C=22A12, dC = AdA, dC = 14 cm 1. a. Find dV in term of dr. What is dV if dr = 0.1cm when r = 10 cm? b. Express the radius r in terms of the volume V. Find dr in terms of dV. Find dr if dV 1 cm when V = 36 cm. = Ans: b.r-v, dr-v dv. dr (2) 36 0.190. = 2. a. Find dS in term of dr. What is dS if dr = 0.1cm when r = 10 cm? b. Express the radius r in terms of the surface area S. Find dr in terms of dS. Find dS if dV 1 cm when V = 36 cm. Ans: a. dS=8xr dr, ds = 8 cm 3. a. Find volume V in terms of the surface S. Find dV in term of dS. What is dV if when S = 16x cm and that dS = 1 cm? b. Find the surface S in terms of the volume V. Find dS in terms of dV. Find dS if V = 36 cm and that dV = cm. 2