Iowa State University



MATH 165 Practice ExamSupplemental Instruction Practice ExamThe following graph is the function f(x). Find the following information.limx→-3f(x)f(-3)limx→-1-f(x)limx→-1+f(x)limx→2+f(x)limx→2-f(x)limx→1+[f(x+1)f(x-2)]limx→1-[f(x+1)f(x-2)]Find the limits or prove it does not exist.limx→∞x7-2x4+x8-3x3+x2-2x3+x2-9x7+12x6+6x5+4limx→∞x7-2x4+-3x3+x2-2x3+x2-9x7+12x6limx→0x3-x+9limx→0x|x|Find the tangent line of the following equation.fx=5x @ x=12Using the formal (limit) definition of a derivative, find the slope of the tangent line of the following function.fx= 2x3-1 @ x=2Find dydx of the following equations.y=x+2x7x-4x2y=(1+x3)(x-3-23x)Find dfdx of the following equations.fx=tanxcotxfx=6+4xcscxFind dwdz of the following equations.wz=1+e-2zz+tan12zwz=31-8z3Determine the following.d4dx4[7sinx3+cos1-2x]d3dx3[45x3-18x2-x ]The position of a tennis ball is given by the function xt=2t+t2e-t for t=[0,4]. Find the following information.Position at t=3 seconds.Velocity at t=1 second.Where the velocity is zero.The time frame that the ball is moving away from the ground.The velocity of an object is measured in m/s. It is given by the equation: vt=(4-t2)(t+2)Find the following information.Find the secant line from t=[2,4] seconds. What is this that you find? Use appropriate unitsFind the acceleration of the object at t=1 second with appropriate units. ................
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