Find the area of the shaded region. AY 2+ L -3 + + 2 3 square units y=x-2 34 y=√x ✈X

Q: Evaluate the limit sin 3x 8x lim x→0

A: given limit

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: 2.) Evaluate the function for the given value of the independent variable. Simplify your answer if…

A: Note: As per our guidelines, we can solve first question. But I solved first two as your first two…

Q: y 4 -3- N f 12 3 et u(x) = f(x)g(x) and v(x)=f(x) g(x) (a) Find u'(1). 9 45 6 X

A: Given that  u(x)=f(x)g(x) and (a) u'(1)(b) v'(5)

Q: Consider the following two lines in space 1 2 = 6t , y =ut y = 4 +5₁ 2 = −1+S 72=X :17 2₂: X=15

A: Given that the following two lines in space

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A: The given expression is:

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Q: Evaluate the following limits. 8,181,818 14231x¹330³811891 f(x)= 4x +33, x≤-9

A: given function

Q: Determine, with justification, whether the series converges absolutely, converges conditionally, or…

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Q: Let h(x) = x² + 2x − 6 - Determine the equation of the tangent line to h at x = 7. Report the…

A: We have given a function -6Put 7Point : Differentiating equation with respect to xPut Slope(m)=

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A: According to company policy we are allowed to provide solution for only first 3 sub parts. If you…

Q: 5. Find the length of the curve f(x) = = √9t¹ - 1 dt on the interval 2 < x < 3.

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Q: 30,000 Р Suppose that the demand function for a product is given by D(p)=- a) Find the demand as a…

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Q: Evaluate the integral. 2 + 1 dx

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Q: a. Find the solution to the initial value problem lim y(t) = t-30 y'e +3 y b. Discuss the behavior…

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Q: 21. (1.4.4) Use the Law of Exponents to rewrite and simplify the expression. a) b) x²n * x³n-1 xn+2…

A: (a)The expression is .Calculation:

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Q: 6. Determine any possible functions f and g, where f g , but such that f is the derivative of g, and…

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Q: Verify that f has an inverse function. Then use the function f and the given real number a to find…

A: We have to find the inverse function of the given function.

Q: Find u and if u-27= (1,3,3) and 37+7=(3, 2, 16).

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Q: Critical Thinking Question: to be agreed upon by the group, and written below by the recorder.…

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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

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Q: For the linear differential equation y' + 6xy = x¹e the integrating factor is: [ After multiplying…

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Q: erify that f has an inverse function. Then use the function f and the given real number a to find…

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Q: Use logarithmic differentiation to find. ○ A) dy = 3 (²)² 2 dx sinx O B) 4 = ()() 3 (senx)² (cost dy…

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Q: Find an equation of the plane consisting of all points that are equidistant from (2, -3, 4) and (-4,…

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

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Q: Parametrize the curve described by the equation y = parametrization to find the length of the curve.…

A: To find the exact length of the curve described by the parametric equations, we will use the formula…

Q: d 4. Determine sin√x dx Space on next page in radical form]

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Q: Find an equation of the tangent line to the graph of the equation at the given point. x² + x arctan…

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Q: 14. (1.3.28) Given the functions Find a) f + g b) f-g c) fg f(x)=√3 x g(x) = √√√x² - 1

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Q: Differentiate. f(x) = e* sin(x) + cos(x)

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Q: Find the time it takes for $9,800 to double when invested at an annual interest rate of 5%,…

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Q: Determine, with justification, whether the following series converges: 4 9. Σn=1 √n

A: To determine with justification, whether the following series converges.

Q: Without a calculator, identify the given key features of the polynomial and sketch a possible graph.…

A: The given polynomial equation is

Q: f(x) = x² - 2x + 7, Need Help? Read It + 9 + h) — f(9) h f(9 "T h = 0

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Q: Kitty starts riding her tricycle 3 ft from her front door; her distances s from her front door 6. t…

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Q: TC arctan(x + y) = y² + (1, 0) Step 1 TC To find the equation of the tangent line to the graph of…

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Q: . Find the x-values in [0,2π) where y = 3 cos x sinx has a horizontal tangent

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Q: 15. (1.3.36) Find fogoh, where f(x) = |x4| g(x) = 2x h(x) = √(x)

A: To find , where

Q: if f'(x) = 5 - (8/x^2) , x≠0, find the value of f(4) given that 2f(1) = 4 + f(2)

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Q: Determine, with justification, whether the following series converges: 1 12. Σ=0 7+3

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Q: Determine whether the function is continuous and differentiable at x = 2. If a y-value is undefined…

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Q: tan(x) (b) lim x→/3 cos(x)

A: given limit

Q: Find an equation in cylindrical coordinates for the rectangular equation x +ỷ =5y

A: Consider the rectangular equation