Find the unit tangent vector to the curve at the specified value of the parameter. r(t) = 3 sin(t)i + 6 cos(t)j,

Q: Select the graph of a function with the given properties. lim f(x) = 2, lim x→ ∞ x→6 lim f(x) = 2, f…

A: Given properties of function

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Q: 6. A fisheries biologist is stocking fish in a lake. She knows that when there are n fish per unit…

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Q: Approximate both ln(0.99) and ln(1.01) using one tangent line approximation: First note that…

A: Using tangent line approximation, we can find the required values.

Q: d) lim √2-x X-2+ 4 e) lim (¹2) x-3x-2

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Q: This is helpful. But clarification needed.  Was the equation computed as 1n or ln? Because it should…

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Q: Use the Chain Rule to find dw dt 3 t 11/23 " where w = sin 8x cos 3y, x = and y=t5.

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Q: Rewrite the expressions as a single logarithm. 4log3x + log3 x - 9 log; x X

A: We have to rewrite this expression as a single logarithm.

Q: Consider the functions f (x) = √√ and g(x) = x - 10. a. Find (f + g) (x) and determine its domain.…

A: Given,

Q: Year Percent 1975 56 1980 59 1985 58 1990 70 1995 76 2000 2004 88 89 Let f(t) be the capacity (in…

A: Let f(t) be the capacity (in percent) at which U.S. nuclear power plants are working at t years…

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Q: Find the equation of the tangent at the given point: y=x²³ −2x² +4 at (2,4

A: x3+4

Q: Let dy Then dx -1 y = tan ¹ (√4x²

A: Let To find .

Q: The pressure P and volume V of an expanding gas are related by the formula PVb = C, where b and C…

A: Product rule of differentiation:

Q: Find the maximum and minimum values of the function f(x, y) = x²y subject to 3x² + 2y² = 18 Please…

A: The given objective function is Subject to constraint: Let

Q: 4. Find the following limits. If the limit does not exist, write DNE and explain -∞o, write that.…

A:

Q: 4. A sphere x² + y² + z² ≤ 4a² has a hole drilled through it in the shape x² + y² ≤ 2ax. How much of…

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Q: 1. Given the equation that describes 1 y=-(x-2)² +27, determine: a) the vertex b) the domain and…

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Q: Find the derivative of the function. 1 + x 1- x y' = y = arctan

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Q: Y=e^x sec x, then dy/dx =

A: .

Q: A particle moves with position function s = t4 - 4t³ - 20t² + 25t, t≥0 At what time does the…

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Q: • find the value of the constant. A so that y= A sin 3t satisfies the differential equation y² +21=5…

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Q: Find the angle between u and v in radians. Round to the nearest hundredth of a radian.u=-4i-7j,…

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Q: УА 1+ -1 0 O 1 Based on the graph shown, which of the following statements is true? O a. The…

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Q: Find the linear approximation L(x) to y = f(x) near x = a for the function. L(x) = f(x) = sin(x), a…

A: L(x) =f(a)+f'(a)(x-a) .

Q: 23. Time-lagged flights An airliner passes over an airport at noon traveling 500 mi/hr due west. At…

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Q: The function y=x² − 3x² +4 has an x intercept at:

A: Consider the function

Q: If the derivative for g(x) = at (3, 4) is 2. Find the equation of the tangent line to g(x) at (3,4).

A:

Q: Approximate cos(1.5) using a quadratic approximation:  First note that cos(1.5) ≈ cos(pi/2). Let…

A: To approximate cos(1.5) using a quadratic approximation.

Q: 3. Graph the Exponential Distribution equation f(x): = .8e-8x

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Q: A DNA sequence consists of a string of elements called nucleotides, in a defined order. Suppose the…

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Q: FRQ (No Technology) The function f(x) is defined as f(x) = -2(x+2)(x-1)² on the open interval (-3,…

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Q: Find the derivative of the function at P0 in the direction of u. f(x,y)=4x2+3y, P0(7,10), u=3i-4j

A: f(x,y)=4x2+3y, P0(7,10), u=3i-4j

Q: Find the number of terms in the series +8 -12 +18 - ... -307.546875

A: The given series is .The aim is to find the number of terms in this series.

Q: Find a formula for ƒ¯¹(x) if ƒ(x) = = (²+1)* ƒ-¹(x) = (-¹)'(z) =

A:

Q: Find the derivative of the function. y = tan-¹(√x- X-8 y' = 1 X

A:

Q: 12. The position function of a particle is given by s(t) = 2t³ - 6t² + 37t + 1, where time, t, is in…

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Q: The equation of motion of a particle is s = t³ - 27t, where s is measured in meters and t is in…

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Q: Which of the following is the correct form of the partial fraction decomposition of x-1 x³ + x DA. A…

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

A: To find an equation of the tangent line to the following curve at the point .

Q: If a rock is thrown vertically upward from the surface of Mars with velocity of 15 m/s, its height…

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Q: 2. Use substitution to factor 3(x-1)² - 4(x-1)-7.

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Q: Find the derivative of the function. h(x) = 3 e⁹x+x70 +70 h'(x) =

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Q: Find the intervals on which f is increasing and the intervals on which it is decreasing. 3 f(x) =…

A: we need to find out the intervals where the function is increasing and the interval where the…

Q: The integral in this exercise converges. Evaluate the integral without using a table. 50⁰ 0 3dx (25…

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Q: If x² + y² + z² = 9, dz dt dx dt X dy = 4, and dt dz = 6, find dt when (x, y, z)= (2, 2, 1).

A:

Q: Evaluate the integral using the following values. 8 8 8 [³x³ dx = 1,020, [²x dx = 30, [° dx = 6 8…

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Q: Represent the plane curve by a vector-valued function. (There are many correct answers.) 3x + 8y −…

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Q: At a given moment, a plane passes directly above a radar station at an altitude of 6 km and the…

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Q: Find the limits for the graph shown below. 1 0 X

A: In this question, we will find the limit of the function when x tends to infinity.