Calculus Homework Answers & Questions Page 7

• 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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• How do you use the limit definition to prove a limit exists?

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• How to evaluate lim x->1 [1/(1-x) - 3/(1-x^3)] and lim x->1 (x^n-1)/(x-1)?

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

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• What is the integral of ##xe^x## from -infinity to 0?

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• What is the derivative of ##y=arctan(4x)##?

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• How do you find a vertical asymptote for y = sec(x)?

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• How do you find the integral of ##(t)sec^2(2t)dt##?

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• What is the difference between Intermediate Value Theorem and the Extreme Value Theorem?

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• What is calculus?

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

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• What's the difference between jump and removable discontinuity?

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• What is the taylor series of ##xe^x##?

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• What is the integral of ##(cos^2x) / sinx##?

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• What is the integral of ##cos2(theta)##?

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• What is the second derivative of ##xe^(2x) ##?

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• What is the McLaurin series of ##f(x) = sinh(x)?

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• What is the smallest possible value of the sum of their squares if the sum of two positive numbers is 16?

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• How do you write a sum in expanded form?

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• How do you find the second derivative of ##sec^2 (2x)##?

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• What is Infinity?

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• How do you use part 1 of Fundamental Theorem of Calculus to find the derivative of the function ##y=int (6+v^2)^10 dv## from sinx to cosx?

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• What is the limit as x approaches 0 of ##arctan(ln(x))##?

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