Calculus Homework Answers & Questions Page 9

• How do you graph ##f(x)=sinx-sqrt(3)cos x## for x is between [0, 2pi ]?

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• Is there any relation between, 1) Tangent ratio in trigonometry & Tangent of Circle? 2) Secant ratio in trigonometry & Secant of Circle?

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• How do you find the derivative of ##(cos x)## using the limit definition?

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• How do you find the derivative of ##ln(sin^2x)##?

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• How do you find the point (in the first quadrant) on the lemniscate ##2(x^2+y^2)2=25(x^2−y^2)## where the tangent is horizontal?

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• What is the derivative of ##e^(2x+1)?

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• What is the concavity of a linear function?

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• A farmer owns 1000 meters of fence, and wants to enclose the largest possible rectangular area. The region to be fenced has a straight canal on one side, and thus needs to be fenced on only three sides. What is the largest area she can enclose?

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

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• How do you find an equation of the tangent line to the curve at the given point if ##y = sec (x) - 2 cos (x)## and ##p=(pi/3, 1)##?

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• How do you find the derivative of ##cotx##?

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• How do you find the integral of ##int (lnx / sqrt(x)) dx## from 0 to 1?

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• How do I simplify ##sin 45 cos 15 + cos 45 sin 15 ## with the angles in degrees?

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• How do you find the derivative of ##cos(pi x)##?

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

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• What does average rate of change mean in calculus?

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• Find the area of the yellow shaded area govern the larger pentagon side ##s=5.5## and area of the smaller pentagon (green) ##A_(pentagon) = 7.59 cm^2##?

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• How to use the alternate definition to find the derivative of ##f(x)=sqrt(x+3)## at x=1?

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• What's the integral of ##int [ ( secx ) / ( 1+ tanx ) ] ^2 dx##?

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• How do you graph the function ##y=5x-x^2##?

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• How do you determine whether the function ##f(x) = xe^-x## is concave up or concave down and its intervals?

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• How do you find the derivative of ##y=ln(5x)##?

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• What is the antiderivative of ##ln(x)^2+x##?

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• How do you find the derivative of ##y=sin2x-2sinx##?

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• How do you find the integral of ##int sec^2(5x)dx##?

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• What is continuity at a point?

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• Let R be the region in the first quadrant bounded by the graph of ##f(x) =sqrt(1+e^-x), the line x=2 and the x-axis, how do you use the trapezoidal rule with n=4 to approx the area?

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

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• How do you use the definition of continuity and the properties of limits to show that the function ##g(x) = sqrt(-x^2 + 8*x - 15)## is continuous on the interval [3,5]?

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• What is the integral of ##ln(sqrt(x))##?

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• How do you find the slope of the tangent to the curve ##y^3x+y^2x^2=6## at ##(2,1)##?

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• For what value of ##k## will ##x+k/x## have a relative maximum at ##x=2##?

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• What is the difference between a definite and indefinite integral?

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• How do you Use the trapezoidal rule with four equal subdivisions to approximate a definite integral?

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• How do you find the rate of change of y with respect to x?

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• What is the integral of the error function?

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• How do you find the volume of a pyramid using integrals?

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• How do you determine the concavity of a quadratic function?

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• What is the derivative of ##y=sec^2(2x)##?

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• How do you evaluate the inverse function by sketching a unit circle, locating the correct angle, and evaluating the ordered pair on the circle for: ##tan^-1 (0)## and ##csc^-1 (2)##?

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• How do you find the multiplier for the rate of exponential decay?

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• A plane flying horizontally at an altitude of 1 mi and speed of 500mi/hr passes directly over a radar station. How do you find the rate at which the distance from the plane to the station is increasing when it is 2 miles away from the station?

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• How do you find the average rate of change of a function over an interval?

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• How do you find the relative extrema for ##f(x) =2x- 3x^(2/3) +2## on the interval [-1,3]?

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• How do you find the linear approximation of ##(1.999)^4## ?

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• How do you evaluate the integral of ##cscx dx## between the interval ##[pi/2,pi]##?

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• How do you find integral of ##((secxtanx)/(secx-1))dx##?

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• What is the power series of ##f(x)= ln(5-x)##? What is it's radius of convergence?

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• A box with a square base and open top must have a volume of 32,000cm^3. How do you find the dimensions of the box that minimize the amount of material used?

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• How do you find limits using a graph?

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