1) Find the area (in square units) of the region under the graph of the function f on the interval  [−11, 9],using the Fundamental Theorem of Calculus. Then verify your result using geometry. f(x) = 9

Q: For the following polynomial function f(x)= x³ + 2x2-x+1, find the lower bound within which all of…

A: f(x)=x3+2x2-x+1

Q: Graph the equations and shade the area of the region between the curves. Determine its area by…

A: To graph the equations and to shade the area of the region between the  curves . To determine the…

Q: When traffic lights are installed, planning must include the duration of the green and the yellow…

A: Given: d=1.5tv+0.06v2 Speed limit=v=45 mph=0.0125 miles/s Reaction time= 1 sec

Q: Evaluate ³da-a³dy, where C' is the boundary of the region between the circles z² + y² = 9 and dx x²…

A: We have to evaluate the integral. We will use Green's theorem to evaluate the integral.

Q: Question 13. A quadratic function is a function p: RR which can be written in the form p(x) = ax² +…

A: SOLUTION:-   Given,  A quadratic function is a function p: R→R which can be written in the form…

Q: Write the composite function in the form f(g(x)). [Identify the inner functionu = g(x) and the outer…

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Q: 7. Evaluate the following expression: 10! 6! 4!

A: => 10!/(6!.4!)

Q: 5. Graph the equations and shade the area of the region between the curves. If necessary, break the…

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Q: Use algebra to evaluate the following limits. x-6 lim a) x6 3x² - 12x - 36 lim b) x-0 x² + 2x² + 7x…

A: Make the factor or cancel the term for finding the limits .

Q: Application - Medicine The concentration, in micrograms per milliliter, of a particular medication…

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Q: A space ship is to be launched from the surface of Venus, which has a radius of about 3760 miles and…

A: Given that,  radius (R) = 3760 miles = 3760 * 5280 ft = 19852800 ft. Surface gravity  (g) = 29.1…

Q: Estimate the area under the graph of f(x)= 1/x+2 over the interval [1,3] using eight approximating…

A: To find out the area using right endpoints and left endpoints with 8 rectangles.

Q: Find the area of the region bounded by the curve y=x2 -1 and the line y=15

A: To find the area of the region bounded by the curve y=x2-1 and  the line y=15.

Q: 31. 8th term is 8; 20th term is 44

A: 31. 8th term is 8; 20th term is 44.

Q: An invasive population of 40,000 Nutria is being hunted in a local swamp. The amount of Nutria…

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Q: 5. Write the first 4 terms of the sequence defined recursively. d₁d-1-1 d₁ = 30 =

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Q: this problem, p is in dollars and x is the number of units. The demand function for a certain…

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Q: Problem 6. Use the divergence theorem to find the outward flux fF.ds = for F (15x2y, x³z, y2) and D…

A: SOLUTION:-     Divergence theorem says that the flux of a vector field F through a closed surface S…

Q: An air freshener starts with 23 grams and evaporates. In each of the following cases, write a…

A: The initial amount=23 grams.

Q: Use the precise definition of  to prove it again

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Q: x²+1 Which of the following is the correct expression of integral (x²+3)(x+2) of partial fractions?…

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Q: x)G(x) and Q(x) = F(x)/G(x), where F and

A: here f(3) = 4;     f(8) = 5; write the equation of function f(x) from point(3,4) to (8,5).  y = mx…

Q: Graph the equations and shade the area of the region between the curves. Determine its area by…

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Q: Evaluate the indefinite integral: 5x+4x³ (x5+x4)³ dx S J +C

A: The indefinite integral is ∫5x4+4x3x5+x43dx

Q: he polynomial of degree 4, P(x), has a root of multiplicicity 2 at x=4 and roots of multiplicity 1…

A: The polynomial of degree 4, P(x), has a root of multiplicicity 2 at x=4 and roots of…

Q: Use the graph of f(x) to determine the following limits. The domain of f(x) is x E R. If the limit…

A: Graph

Q: Find the two vectors that satisfy the given conditions: (1) The unit vector whose dot product with…

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Q: Given f(x, y) = 6x4 — 1x²y6 + 2y³, find fz(x, y) = y) = fy(x, fzz(x, y) = fry(x, y) =

A: The function isfx,y=6x4-1x2y6+2y5

Q: The Intermediate Value Theorem guarantees the existence of a real zero of a polynomial function as…

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Q: The function f(x)= (x+5) is one-to-one. a. Find an equation for f(x), the inverse function. b.…

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Q: Find the unit tangent vector N(t) to the curve r(t)= when t=0

A: r(t)=<sint, t, cost>, t=0

Q: tangular coordinates of a point are given. Plot the point. (Select the correct graph.) (0, -3) 2 -2…

A: (0,-3)

Q: i. ii. the length of the perimeter of the site. the total area of the site to be developed. 29.5m…

A: SOLUTION:-   Given that we have surveyed one of the buildings sites which your company is to…

Q: Find the exact solution of the exponential equation. 78t = 39 || || X

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Q: Aside from L Hopital Rule, is there any other way? How about using any properties to find limits? In…

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Q: Find the work done by the force field F in moving an object from P to Q. F(x, y) = e-Yi-xe- j P(0,…

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Q: Let A(x) = f* f(t) dt, where f(a) is the function shown to the right. Answer the following questions…

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Q: PROBLEM NUMBER 18 Estimate the area of the region between f(x) = x³ - 2x² + 4 the x-axis on [1,4]…

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Q: Suppose that is the finite region bounded by f(x) = √x and g(x) = 3 R Find the exact value of the…

A: For the two function f( x ) and g( x ) ( a ) the volume of the region obtained by rotating the…

Q: (a) Determine x³+y³ f₁xıyı = { x=y² 1 9 (b) If if f f is is if x*y² , otherwise continuons…

A: We need to check if given function is differentiable and continuous.

Q: find the unit tangent vector t(t) to the curve r(t)= when t=0

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Q: A rectangular playing field lies in the interior of an elliptical track that is 60 yards wide and…

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Q: 56. Reunte each expression as a Answer: single loganthm: 31n (x) + In (y-1)

A: let  H=3lnx+lny-1

Q: Use the Shell Method to compute the volume of the solid obtained by rotating the region underneath…

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. h(x) = 2…

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Q: 2 3 ( - 1²/1 ) ² 3 lim 3 X→∞ x

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Q: and x = 4. y 15 10 5 -5 Find the area of the re -10- 2 4 X

A: To find the area of region bounded by given curve. Given y = -x2 + 8, y=x2 , x = 0 and x = 4.

Q: 53. Determine if the series is absolutely convergent, conditionally convergent, or divergent. (-1)k…

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Q: 3. Write the quadratic polynomial x² - 6x +1 in standard form CAKA vertex form)

A: