| Question 1. Integrate (x-5)e^x. dx |
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| Question 2. Given f(x) = (x+2) (x-3)^4, find df/dx and d^2f/dx^2 |
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| Question 3. Find the dimensions that will minimize the surface area of a rectangular box, open on top, with volume of 48 cubic inches |
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| Question 4. Find the relative extrema of the function f(x)= 6+x^4-5x^2. List your answers in terms of an ordered pair. Then sketch the graph of the function. |
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| Question 5. Evaluate for g (x) = x square+x ,
g(x+h)-g(x) / h |
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Not Avalable
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| Question 6. Express the distance between the point (3, 0) and the point P (x, y) of the parabola
y = x2 as a function of x. |
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| Question 7. ABCD is a rhombus with AB=5cm and angle BAD=30 degrees. Find its area. Please include working |
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| Question 8. Sketch the translated circle 4x2 + 4y2 - 4x + 12y = 15. Indicate the center and radius |
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| Question 9. Use Newton's method to find the solution of the equation x2 + 4x – 1 = 0 in the interval [0, 1] accurate to four decimal places. |
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| Question 10. Ticket Sales- Tickets for a concert were sold to adults for $3 and to students for $2. If the total receipts were $824 and twice as many adult tickets as student tickets were sold, then how many of each were sold? |
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| Question 11. The base of a triangle is (2x+3) feet long and the height is (x+3) feet long. If the area of the triangle is 27 square feet, find the base and height of the triangle. |
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| Question 12. Corporate Taxes- According to Bruce Harrell, CPA, the amount of federal income tax for a class C corporation is deductible on the Louisiana state tax return, and the amount of state income tax for a class C corporation is deductible on the federal tax return. So for a state tax rate of 5%and a federal tax rate of 30%, we have
State tax = 0.05(taxable income- federal tax)
And
Federal tax = 0.30(taxable income – state tax)
Find the amounts of state and federal income tax for a class C corporation that has a taxable income of $100,000. |
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| Question 13. Find dx/dt given x = the square root of (1+cot3t). |
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| Question 14. Find dy/dx given y = 1/ (3x-2)^3. |
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| Question 15. Calculate the angle between the given vectors. Also calculate the angles between the first vector and each of the coordinate axes.
A = <1, 2, 3> B =<-2, 4,-1> |
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| Question 16. Find the trigonometric limit: lim sin3x/2x x->0 |
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| Question 17. Determine whether u and v are orthogonal, parallel, or neither
u = < -12, 30 >
v = <1/2, -5/4> |
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