Find all points (x, y) on the graph of y = x2 −6 with tangent lines passing through the point (3, 2); then find the equation of the tangent line corresponding to the smaller x-value.

Q: An open-top rectangular box is being constructed to hold a volume of 350 in³. The base of the box is…

A: Given: volume = 350 in³ base material costing = 6 cents/in² front cost = 12 cents/in² remainder…

Q: Let f be the function given by f(x)=sin(2x)cos(1+x). What is the average value of fon the closed…

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Q: The Seventh Gate As you approach the seventh gate, you notice that it is only a short distance to…

A: The given function is;  f(x)=sqrt(4-34x).

Q: Find an equation of the tangent line to the curve at the point (1, 1). In(xex6) y = y =

A: The given equation is;  y=ln(xex^6).

Q: The average rate of change of f(x) = X a. 2 b. 0.5 over the interval 1 ≤ x ≤ 2 is c. -0.5 d. -1

A: we will find the required.

Q: Find an equation of the tangent line to the curve at the point (1, -1-). y = x³e-x y =

A: To Find: Tangent line to y=x3e-x, at point 1, 1e

Q: In this problem, p is in dollars and q is the number of units. (a) Find the elasticity of the demand…

A: Given: p+8q=240

Q: 4. Evaluate the limit, if it exists: lim x+1 a. 1 b. -1 x²-3x+2 x-1 c. d. 0 does not exist

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Q: Let S = {1, 2, 3, 4, 5). Let f S S be the function defined by f = {(1, 1), (2, 1), (3, 3), (4, 3),…

A: Sol:- To count the number of functions g: S→ S that satisfy the given condition, we need to first…

Q: Suppose the demand for a certain brand of a product is given by ​D(p)=−p^2 / 416+450​, where p is…

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Q: п Convert the point (p, 0, 0)=(3, 377) 6 expressions, or decimals to at least one decimal place. (x,…

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Q: The graph of y = f(x) has f(5) = -3 and f'(5) = -3. Which of the following might be a graph of y =…

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Q: . Evaluate the limit for the graph: lim f(x). |y4 4 a. 3 b. 2 2 -4-20 2 -2 -++-% x c. d. 5 does not…

A: We will find the required.

Q: 4sqrt(2) was incorrect

A: Given:= f(x,y) = x3y2U = (-3,3) P= (-1,-2)   The directional derivative being negative means that…

Q: Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the…

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Q: Let f(x) = 4x² - 2x4. Find the open intervals on which f is increasing (decreasing). Then determine…

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Q: In this problem, p is in dollars and q is the number of units. Suppose that the demand for a product…

A: Given: Demand for product is given by 2p2q = 30000+9000p2, where p is in dollar and q is the number…

Q: A cable runs along the wall from C to P at a cost of $7 per meter, and straight from P to M at a…

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Q: Find the arc length of the curve y = ln x - ²² on the interval [1,3].

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Q: > Let f(x) be the function shown in the graph below. Click on the graph to enlarge it. Determine the…

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Q: In this problem, p is in dollars and q is the number of units. (a) Find the elasticity of the demand…

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Q: Write an equation of the line containing the given point and parallel to the given line. Express…

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Q: 20,000e 1+ ķ xy-plane, where x and y are measured in centimeters, find the total population of…

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Q: Compute [5t³ - 8t + 1] d dt

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Q: Suppose a product's revenue function is given by -8q² + 800q, where R(q) is in dollars and q is the…

A: The given revenue is Rq=-8q2+800q, where Rq is in dollars and q is the number of units sold. To find…

Q: 6y' - 2y = xy¹, y (0) = -1

A:

Q: Determine whether Rolles theorem can be applied to the function. f(x)=(x-5)(x-6)(x-7) on the closed…

A: we have to slove above question f(x)=(x-5)(x-6)(x-7) on the closed interval [5,7]. find all numbers…

Q: 1 2 √x² x + 10x + 61 S -dx =

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Q: Consider the following vector function. Find each of the following. r'(t) = = r'(0) r(t) = cos(t) i…

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Q: use differentials to approximate the vaule of sqrt(25.1)  A. 5.0300 B. 5.0200 C. 5.0100 D.…

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Q: Find the 4th order Taylor polynomial, T4, of the function f(x) = e³ centered at a = 1.

A: Given function:- fx=e3x

Q: Q14 Find the equation of the tangent line to the curve f(x) = 2x²(x − 3) at x = 1.

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Q: Find the unique solution to the differential equation that satisfies the stated conditio dy In(x) dx…

A: given:differential equation dydx=lnxxy,  y1=6

Q: Find the Maclaurin series and find the interval on which the expansion is valid. f(x) = ln (1-x²)

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Q: Draw an accurate diagram of what follows and find resulting distance to the port: A ship sails on a…

A: We have to find, the distance from the ship to the port and the bearing of the ship from the port by…

Q: Find the derivative

A: We are required to find the derivative of (a) y=cos2tan1+x3(b) f(t)=3csc5πt-71-cotπt5-7

Q: Consider the ellipse 4x² + 2xy + 2y² = 88. (a) The derivative on this curve is dr dy = dx (b) Find…

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Q: Evaluate the integral. 6e6t ¹+12° +35 S- 12t dt

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Q: Given ƒ"(x) = 6x – 5 - and ƒ'(−2) = −1 and ƒ(−2) = 2. Find f'(x) = and find f(2)=

A: We need to find out the value of f'(x) and f(2) for which the second derivative is given.

Q: 43 x

A: given diagram of polar region

Q: Use a differential to approximate. (Give your answer correct to 4 decimal places.) 4(3.98) (3.98)² +…

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Q: Consider the following problem: a farmer with 650 feet of fencing wants to enclose a rectangular…

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Q: The Map As you walk through Gate 4, you realize that Gate 5 is nowhere to be found. In front of you…

A: Given f( x ) is continuous in the given domain If a function is continuois at x = a then limx→a-f( x…

Q: Find the average value of f(x,y) = sin (x + y) over 0≤x≤/3, 0≤ y ≤5/3 0 ≤x≤2/3,0 ≤ y ≤7π/6 a. the…

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Q: b) lim x² +8x+16 X-1 x²-16

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Q: Does the series convergence or diverge 7 n²+5n+6 ∞

A: We have given a series  Let, y=∑n=0∞7n2+5n+6 Using factor form n2+5n+6=n2+2n+3n+6=nn+2+3n+2…

Q: Differentiate the function. f'(x) = f(x) = In(cos(x))

A: The solution is shown below-

Q: Question 19 ( ) Let f(r) Inz for all z>0. Determine all intervals on which is decreasing.

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Q: 19x² tan¹x dx = [

A: The given integral is 19x2tan-1x.

Q: The radius (R₁) of one ball bearing is 1.0 mm greater than the radius (R₂) of a second ball bearing.…

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