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Q: Find an equation of the tangent line to the given curve at the specified point: 4, x + 3 y =

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Q: f is a continuous function and x>0. Find the value of f(1) for the equation in the figure.

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Q: Evaluate the integral using the indicated trigonometric substitution. (Use C for the constant of int...

A: Consider the integral

Q: Betty and Bob Widget Company employs labor (workers) and uses capital (money) to produce output (wid...

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Q: Please help with #2. I need to solve for the Unit tangent vector "T", the Unit Normal Vector "N", an...

A: Find the unit tangent vector:

Q: f(x)=(7-5x)e^x (D) List the x values of all local maxima of f(x). If there are no local maxima, ente...

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Q: Find the following limits: (a) If lim x--> 3 ((?f(x)/2x) +1)?=2,find lim x→3 f(x) (b) Find lim x...

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Q: Using long division, you can calculate that 2x3 – 16x² + 7x – 37 R(x) Q(x) + 2x2 + 5 | f(x) = 2x2 + ...

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Q: The function y(x) is defined by the implicit equation x2−√ylny=1. Find its differential at the point...

A: Differentiate both sides with respect to x and solve for dy/dx

Q: A particle moves along the curve r(t)=⟨t2,t2−4t,t⟩. Find the minimum speed of the particle.

A: A particle moves along the curve The velocity of the particle at any time t is Now, speed of the p...

Q: Find the area of the region bounded by the graphs of y2=1-x and 2y= x+2.

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Q: Let f(x)=x^3−15x^2+27x+4. Find the open intervals on which f is increasing (decreasing). Then determ...

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Q: Find the maximun and minimun of P= 4x + 3y subject to: ...

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Q: A cylindrical tank has a height 8 m and a radius 2 m. Suppose the water tank is half- full of water....

A: The amount of work required to pump water from each slice out of the top of the tank,

Q: Verify the conditions of Alternating series test. Hence, determine the convergence or divergence of ...

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Q: 8. -0.05t Solve: 30+2te 91

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Q: tan z lim Is Select one: a. 1 b. e C.-1 d. 0

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Q: x³ In(x) dx

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Q: 1. What should be A for the path independent of (2,4) ry + A 2Ay – x dy. y? -dx + (1,2) Moreover eva...

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Q: Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable?...

A: f(x) = x4 − 81x is a polynomial function.

Q: The area of the region between the graphs of y = x² and y = -x from x = -1 to x = 0 is O is Li (2² +...

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Q: The value of (8.1)/ .

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Q: Suppose the supply of x units of a product at price p dollars per unit is given by p = 20 + 40 ln(2x...

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Q: Suppose that f(x)=x^3−3x^2+3. (A) List all the critical values of f(x). Note: If there are no critic...

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Q: Sketch the graph of the function f whose derivative has the given graph

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Q: Let f(x)=(x−4)/(x+6). Find the open intervals on which f is increasing (decreasing). Then determine ...

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Q: Use linear approximation to approximate v49.4 as follows. Let f(x) = Vx. The equation of the tangent...

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Q: If f is integrable on [a;b], then f2 is integrable on [a;b]. This statement however is false for the...

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Q: IF ƒx(a, b) = ƒy(a, b) = 0, must ƒ have a local maximum or minimum value at (a, b)? Give reasons for...

A: ƒx(a, b) = ƒy(a, b) = 0, is necessary but not sufficient condition for ƒ have a local maximum or min...

Q: Suppose the supply of x units of a product at a price of p dollars per unit is given by p=20+40ln(2x...

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Q: 100 S -0.05+ Solve: S 30 + 2te dt

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Q: Chapter 4, Section 4.4, Question 007 Let C(9) represent the cost, R(g) the revenue, and T(g) the tot...

A: Let C(q) represents cost and R(q) represents the revenue function. Then, profit function is given b...

Q: Let A and B be constants. Prove that ifA > 0, then all solutions of dy/dt+ Ay = B approach the sa...

A: On some rearrangement you will get,

Q: Suppose that f(x)=x^3−3x^2+3. (E) List the x values of all local minima of f(x). If there are no loc...

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Q: 20 value of E,(k+ 5)?.

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Q: d?y Find by implicit differentiation when dx? 5xy – y? = 9

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Q: Let 1 f(x) = sin (x) = Let 1 (x)6 sin x '(x) =

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Q: The line y = -4x + 16 is tangent to the graph of 100 y : x + 6 at the point help (points)

A: Given the equation of a tangent line: