A PREVIEW OF CALCULUS SECTION 2.1. WHAT IS CALCULUS? The mathematics of change.  Velocities  Accelerations  Tangent lines  Slopes  Areas  Volumes.

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Presentation transcript:

A PREVIEW OF CALCULUS SECTION 2.1

WHAT IS CALCULUS? The mathematics of change.  Velocities  Accelerations  Tangent lines  Slopes  Areas  Volumes  Arc lengths  Centroids  Curvatures  Etc

EX. 1 Find the value of f(x) when x = c With Differential Calculus… Find the limit of f(x) as x approaches c.

EX. 2 Find the slope of a line. With Differential Calculus… Find the slope of a curve.

EX. 4 Find the average rate of change between t=a and t=b. With Differential Calculus… Find the instantaneous rate of change at t = c

EX. 5 Find the curvature of a circle. With Differential Calculus… Find the curvature of a curve.

EX. 6 Find the height of a curve when x = c. With Differential Calculus… Find the maximum height of a curve on an interval

EX. 7 Find the tangent plane to a sphere With Differential Calculus… Find the tangent plane to a surface.

EX. 8 Find the direction of motion along a line With Differential Calculus… Find the direction of motion along a curve.

EX. 9 Find the area of a rectangle With Differential Calculus… Find the area under a curve.

EX. 10 Find the work done by a constant force With Differential Calculus… Find the work done by a variable force.

EX. 11 Find the center of a rectangle With Differential Calculus… Find the centroid of a region.

EX. 12 Find the length of a line segment With Differential Calculus… Find the length of an arc.

EX. 13 Find the surface area of a cylinder With Differential Calculus… Find the surface area of a solid of revolution.

EX. 14 Find the mass of a solid of constant density With Differential Calculus… Find the mass of a solid of variable density

EX. 15 Find the volume of a rectangular solid With Differential Calculus… Find the volume of a region under a surface

EX. 16 Find the sum of a finite number of terms With Differential Calculus… Find the sum of an infinite number of terms