(a) Let f (x) = Vx – 1. Use the limit definition of the derivative to find f' (x).

Q: x3 dx Vx² + 9

A: A detailed solution is given below

Q: A farmer has 1200 meters of fence and wants to construct a rectangular pasture. The pasture will be…

A: Explanation of the answer is as follows

Q: dx (x – 2)vx2 – 4x +3 g) . dx sin-1 x v1-x? h) . cos(sec-1x) dx xVx2 – 1 2/V3

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Q: Lena deposits $40,000 into an account that pays 6% interest per year, compounded annually. Ravi…

A: Given problem:- Lena deposits $40,000 into an account that pays 6% interest per year, compounded…

Q: (a) Find the numbers at which the following function y =f (x) is discontinuous. And at which of…

A: We have to find the continuity and discontinuity points. According to our guidelines we can solve…

Q: after t hours is given by v(t) == 3t"+2t. Find the distance the particle travels during the first 4…

A: Given query is to find the distance in first 4 hours.

Q: Use implicit differentiation to find an equation of the tangent line to the curve at the given…

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Q: Part 1: Let h be the height of AWXY. Find the length of the corresponding base. | cm 14 cm Part 2:…

A: Part 1  as h is height  base is WY length of base = 14 cm

Q: Find the volume of the solid formed by revolving the region bounded by y = x – x and the x-axis (0 <…

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Q: graph of the function arcsec(x).

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Q: x2 - c2 x c -3

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Q: se Exact Differential method (Rule II) to solve : x² – y²)dy = xy dx.

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Q: Use the properties of logarithms to expand the following expression. 5 3 2 Each logarithm should…

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Q: If f(x) = 2/x and g(x) = 4/x, find f(g(x)) and g(f(x)). f(g(x)) = g(f(x)) =

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Q: Find f' (x). i f(x) = 3x10 csc-1

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Q: Find the area of the surface given by z = f(x, y) that lies above the region R. f(x, y) = Va2 – x2 R…

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Q: Find the exact length of the curve. x- 2, y =? - 2, Osts9

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Q: Use the properties of logarithms to expand log Each logarithm should involve only one variable and…

A: The objective of the question is expanding the given function.

Q: 4. Ricardo is taking a trip from Arizona to Yosemite National Park in California. The gas mileage in…

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Q: O False

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Q: f(x) = = hen -6x I+3 f'(3) =?. (Answer accurate to 2 docimal

A: Given f(x)=-6xx+3f'(x)=ddx-6xx+3…

Q: 4. Ln=1 By the series test: 3n-2

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Q: Select the answer option that corresponds with polar coordinates (3, 7). 90° WIN 135° 7 radians 150°…

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Q: Evaluate the iterated integral by converting to polar coordinates. (x² + y?)3/2 dy dx dr de = Jo

A: Follow the procedure given below.

Q: Evaluate the integrals. Use a capital C for any constant term. 5x + 6) dx = Preview syntax error…

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Q: Which of the following series can be used with the comparison test in order to conclu that the…

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Q: (e) In a certain city the amount of violent crime was decreasing but slower than it was in previous…

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Q: A ALEKS - J'Angello Farrington X Messenger www-awu.aleks.com/alekscgi/x/lsl.exe/1 0- う O EXPONENTIAL…

A: Here we are given a function which is defined by the following rule  f(x)= (1/4)-x And gor different…

Q: Determine wnea ther the sequence con verges diverges. Lf It converges Find or its limits. an : cos…

A: Given query is to find sequence converges or diverges.

Q: Set up integrals for both orders of integration. Use the more convenient order to evaluate the…

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Q: Let å = - 5i – 43 and b = - 7ỉ + 23. Find ä · 6

A: This question can be solved using the concept of dot product.

Q: Give some examples of geometric problems that can be solved using the parametric equations of a line…

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Q: Verify Green's Theorem by evaluating both integrals aN aM y2 dx + x2 dA ду ax for the given path. C:…

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Q: Solve this problem algebraically, using your knowledge of derivatives. Do not solve by graphing.…

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Q: Find the gradient of the function at the given point. Function Point f(x, y, z) = V x2 + y2 + z? (8,…

A: Gradient of function fx, y, z=x2+y2+z2 at  point 8, 7, 3

Q: 2. In addition to obtaining the domain and range, provide a sketch of the graph of the following…

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Q: 10. (Section 4.4) Find the area of the region bounded by f(x) = x² + 3x + 1 and g(x) = 6x + 1.

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Q: Find the exact length of the polar curve. r = 3 cos(theta),    0 ≤ theta ≤ pi

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Q: 9 Determine whether the series 9. 9. +...+ 9. +... is convergent or 100 1002 1003 100" divergent. If…

A: 9100+91002+91003+.....+9100n+...common ratio:a2a1=a3a2=1100First term: a=9100common ratio:…

Q: Solve (x² + 1) + 2xy = dy 2 dx x2+1

A: The given equation is;  (x2+1)dy/dx +2xy =2/(x2+1).

Q: Let g(x) = :| f(t) dt, where f is the function whose graph is shown below. What is the value of g'…

A: Let gx=∫0x ft dt, where f is the function whose graph is shown below.To determine the value of g'8.…

Q: Write each pair of parametric equations in rectangular form. Then sketch the curve. 8) x= 4cos t+ 1,…

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Q: Find the general solution of the given linear differential equation. y'''' − 2y''' + 5y'' = 0

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Q: I"f'(x) 0. then which of the following is true? o f(x) is increasing and concave up o f(x) is…

A: If f'(x) &lt; 0 and f''(x) &gt; 0 Then , which of the following statement is true

Q: = [[[In(x² + y² )dxdydz

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Q: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Minimize…

A: Given;  Minimize :(x, y) =x2+y2 Constraint: x+2y-20=0.

Q: Use the properties of logarithms to expand log(xz). Each logarithm should involve only one variable…

A: log(xz6)We know that logab+logac=loga(bc)Therefore,log(xz6)=log(x)+log(z6)we know…

Q: Use the cylindrical shell method to calculate the exact volume of the solid formed by rotating the…

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Q: For the graph of y = f(x) shown to the right, find the absolute minimum and the absolute maximum…

A: The absolute maximum of a given graph is the point on the entire graph with the highest y-value…

Q: 3. Ση-1 -1/m By the e n2 series test:

A: We will solve this problem by Abel's test for series