Calculus Homework Answers & Questions Page 11

• How do you give a value of c that satisfies the conclusion of the Mean Value Theorem for Derivatives for the function ##f(x)=-2x^2-x+2## on the interval [1,3]?

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• What is the formula for the nth derivative of ##sin (ax +b)## and ##cos(ax+b)##?

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• How does the logistic model of population growth differ from the exponential model?

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• How do you find a tangent line parallel to secant line?

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• Do points of inflection have to be differentiable?

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• What is the derivative of ##ln e^(2x)##?

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• How do you integrate: ##cos(lnx) dx##?

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• How do you find the integral of ##(arctan(2x)) / (1+4x^2)##?

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• What is the limit as x approaches infinity of ##arctan(x)##?

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• How do you find the derivative of ##y=arcsin(1/x)##?

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• How do you find a power series representation for ##ln(5-x) ## and what is the radius of convergence?

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• How do you find the turning points of a cubic function?

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• How do you integrate ##int ( (x^2) / (sqrt(4 - x^2)) ) dx##?

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• What is the difference between an infinite sequence and an infinite series?

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• What is the interval of convergence of ##sum (x^(2n) )/( (2n)! )##?

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• How do you find the derivative of ##y=arcsin(2x+1)##?

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• How do you find the derivative of ##y=arcsin(sqrt(x))##?

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• How do you find the area of circle using integrals in calculus?

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• How do you use the Product Rule to find the derivative of ##(x^2)(x^3+4)##?

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• The volume of a cube is increasing at the rate of 20 cubic centimeters per second. How fast, in square centimeters per second, is the surface area of the cube increasing at the instant when each edge of the cube is 10 centimeters long?

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• The altitude of a triangle is increasing at a rate of 1.5 cm/min while the area of the triangle is increasing at a rate of 5 square cm/min. At what rate is the base of the triangle changing when the altitude is 9 cm and the area is 81 square cm?

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• How do you calculate the antiderivative of ##sin(2x)/cos(x) dx##?

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• If ##x^2+y^2=25## and ##dy/dt=6##, how do you find ##dx/dt## when ##y=4## ?

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• What is the integral of ##x^3 cos(x^2) dx##?

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• How do you find the area of the region bounded by the polar curve ##r^2=4cos(2theta)## ?

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• How do you use the binomial series to expand the function ##f(x)=(1-x)^(2/3)## ?

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• How do you find the stationary points of the function ##y=sin(x)##?

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• How do I us the Limit definition of derivative on ##f(x)=tan(x)##?

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• How do you draw the slope field of the differential equation ##dy/dx=1/3(y-1)^(1/3)## ?

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• What is the derivative of ##-csc(x)##?

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• How do you use the Squeeze Theorem to find ##lim (1-cos(x))/x## as x approaches zero?

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• How do you find the derivative of ##sin2x cos2x##?

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• Is ##f(x)=3x^2-x+4## increasing or decreasing at ##x=2##?

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• How to calculate S3,S4, and S5 and then find the sum for the telescoping series ?

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• What is trigonometric substitution and why does it work?

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• What is the opposite of exponential growth?

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• Use a graphing calculator or computer to verify the given linear approximation at a = 0? Then determine the values of x for which the linear approximation is accurate to within 0.1. (Round the answers to three decimal places.) e^x ~= 1 + x

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• How do you find the exact relative maximum and minimum of the polynomial function of ##f(x)= 2x^3-3x^2-12x-1##?

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• What is the definition of logistic growth?

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• How do you verify that the function ##f(x)= (sqrt x)- 1/3 x## satisfies the three hypothesis of Rolles's Theorem on the given interval [0,9] and then find all numbers (c) that satisfy the conclusion of Rolle's Theorem?

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• Is there a systematic way to determine an integrating factor ##mu(x,y)## of the form ##x^n y^m##, given a not-necessarily-exact differential equation?

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• What is the second derivative of ##secx##? 

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• How do you find the derivative of ##y= log x^2##?

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• How do you find the integral of ##sin^2(3x)dx##?

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• What is the integral of ##cos^6(x)##?

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• What is the derivative of ##y=arccos(1/x)##?

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• How do you differentiate ##f(x)=xlnx-x##?

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• A rancher has 1000m of fencing to enclose two rectangular corrals. The corrals have the same dimensions and one side in common (let that side be x). What dimensions will maximize the enclosed area?

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• How do you evaluate the integral of absolute value of (x - 5) from 0 to 10 by finding area?

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• Evaluate ##sum (2n+1)/2^n## from n=0 to infinity ?

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