Find the limit, if it exists, or type N if it does not exist. e√1x²+4y² lim (x,y)→(-4,1) e^8

Q: A volume is described as follows: 1. the base is the region bounded by x=-y² + 8y +28 and x = y² -…

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Q: Q1. Solve the following differential equations: a.1) Consider that x = 1, y = 1 y ²=²-1 X y'

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Q: Determine the open intervals on which the function is increasing, decreasing, or constant. (Enter…

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Q: Use logarithmic differentiation to find dy/dx. dy dx || y = 2 9 V x2 + 9 x>3

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Q: Find the equation of the tangent line 7(x) to the graph of the given function at the indicated…

A: We are asked to find the tangent line of the equation

Q: Consider the differential equation y"-7y'-8y = 0. The characteristic equation is The solution(s) to…

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Q: Refer to the appropriate triangle or trigonometric identity to compute the given value. (Use…

A: Trigonometry identity to compute the given value

Q: Make a sketch of the region and its bounding curves. Find the area of the region. The region inside…

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Q: The integral 27 12xe-x² dx can be done with the substitution u = e X and du = xe X dx.

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Q: ketch a possible graph of a function f, together with vertical asymptotes, that satisfies all of the…

A: We will satisfy each conditions with graph of function

Q: Solve the initial value problem for r as a vector function of t. d²r dt² Differential equation: = -…

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Q: Find the centroid of the region bounded by the graphs of the functions 1 ㅠ and x = and touching the…

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Q: 2. At time t = 0, a tank contains Qo lbs of salt dissolved in 50 gallons of water. Water is 1…

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Q: Q4. Let x denote the grams of gold obtained in a ton of ore. Consider the two events A = {0 < x < 3}…

A: As per our guidelines we are allowed to answer only three subparts of the given problem. Kindly…

Q: e4x + 2e -7x -7x +4e¹ lim I ∞ e ||

A: To evaluate the following limit.

Q: The graph of f(x), a polynomial function, is shown below as a solid blue curve. The dashed curves…

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Q: Let h(y) = − y(y² – 6) Determine the derivative of h. h'(y) Determine the slope of h at y = 0. h'(0)

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Q: If f(x) = 10x + 4, find ƒ'(10). f'(10) =

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Q: 5. Will orders two drinks at a coffee shop. Drink 1 contains 50% espresso. Drink 2 contains 10%…

A: Given TableOunces of LiquidconcentrationOunces of ExpressoDrink 1x0.50Drink 2y0.10Mixture200.25

Q: Use log differentiation to find dy/dx  y=x^6x a) 6x^6x (lnx+1) b) 6x^6x-1 c) 6(lnx+1) d) 6x^5x

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Q: Find the length of the spiral r = 30², 0≤0≤√√32. The length of the spiral is (Type an exact answer,…

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Q: the derivative of the function. y = x√ 16 - x² + arcsin x₁ X 5

A: Derivative of the function .

Q: 10+ 10 5 This curve has equation y = x² + 2x - 3. (Remember this is a non-calculator question!)…

A: The shaded region represents the area covered by the curve with the x-axis in the given interval.The…

Q: For f(x) = (a) fog 4 x-3 1 and g(x) = find the following composite functions and state the domain of…

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Q: Which point is farther from the origin, ( – 1,2, − 1) or (0,0,4)? Select the correct answer below.…

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Q: Find dy/dx by implicit differentiation. Then find the slope of the graph at the given point. (3x +…

A: Given equation is

Q: Find the derivative of P(x) = -8x¹/9 - 3x -7 Write your answer using negative exponents. P'(x) = =

A: Given,

Q: A differential equation is separable if it can be written in the form dy dx where g is a function of…

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Q: * 3 -୯ 5 4 3 2 -1 -3 -4 -5 In the above graph of y = f( x ), find the slope of the secant line…

A: From the graphs, we find the slope of the secant line.

Q: To help get in shape, Zahra gets a new pair of running shoes. If she runs 1 kilometer each day in…

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Q: Suppose that V(t) = (28)1.07⁰ + 5 sin(t) represents the value of a person's investment portfolio in…

A: To find the instantaneous rate at which the portfolio's value is changing on January 1, 2022,  we…

Q: Find the function y=y(x), y>2, which solves the initial value problem 4x2+(dy/dx)=2x^2y y(0)=7

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Q: parametrize the path that follows the graph of the function y=e^x from (0,1) to (1,e)

A: We parametrize the path that follows the graph of the function y=e^x from (0,1) to (1,e).

Q: At the beginning of an experiment, a scientist has 320 grams of radioactive goo. After 75 minutes,…

A: Exponential decay formula in terms of half life can be given as below :Put values

Q: Use the function f and the given real number a to find (f ¹)'(a). (Hint: See Example 1. If an answer…

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Q: Find dy dx dy dx for the given function. y = 3 - cot(x) 3 + cot(x)

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Q: 3x+2 Find the points on the graph of the function y = 2-3 where the tangent line is perpendicular to…

A: Slope of two perpendicular lines The given line is perpendicular to the tangent of the…

Q: a. The function f(x) = x can also be written as x to what power? b. The function g(x) = √√x² can…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Evaluate the limit: lim (3z-5) 24-4 =

A: given infomation

Q: 1. For the following exponential function, construct its table of values and its corresponding…

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Q: Find equations for the tangent line and normal line to the circle at the given points. (The normal…

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Q: 20° A 10 yd S

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Q: An economy's consumer price index (CPI) is described by the function I(t)=-.2t^3+3t^2+100  , where…

A: To find the rate at which the Consumer Price Index (CPI) is changing in 1998 , we need to calculate…

Q: The equation r(t) = (12 sin t) i + (5 cos t)j + (8t) k is the position of a particle in space at…

A: If r(t) is the position vector then velocity vector, v(t) = r'(t)Acceleration vector, a(t) = v'(t)

Q: The point  P(9, −3)  lies on the curve  y = 3/(8 − x). (a) If Q is the point (x, 3/(8 − x)), use…

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Q: The heat index I is a measure of how hot it feels when the relative humidity is H (as a percentage)…

A: Solution-Now we will calculate partial derivative,

Q: eliminate arbitrary constants. Show complete solution. y= Ax + Bx²

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Q: 7. Find the total mass of a circular plate of radius 20 cm whose radial mass density function is…

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Q: Use the theorem of Pappus to find the volume of a torus (pictured here). Assume that a disk of…

A: Given:Disk of radius =&gt; a = 5x= b = 4To determine: The volume of torus.

Q: A toy rocket is launched from a table 2 feet above the ground. The height of the rocket above the…

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