Using implicit differentiation, show that if P is any point on the circle defined by ?2+y2=a2, then the tangent line at P is perpendicular to OP.

Q: Evaluate the integral. Check your results by differentiation. (Use C for the constant of integration...

A: Consider the provided integral, ∫ 8x44x5+6-3dx Evaluate the provided integral. ∫ 8x44x5+6-3dx=8·∫ x4...

Q: The number of ships to arrive at a harbor on any given day is a random variable represented by x. Th...

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Q: Consider the parametric equations below. x = t2 - 1, y = t + 2, -3 sts 3 (a) Sketch the curve by usi...

A: (a) The parametric curve is given by the equation, x=t2-1y=t+2-3≤t≤3 Thus,  the points on the curve ...

Q: If f(x) = 5x2 - 6x + 1, find [f(x + h) - f(x)]/h.

A: The given function is f(x) = 5x2 - 6x + 1

Q: Calculate v2 – li. Give your answer in a + bi form. In polar form, use the angle 0 < 0 < 27. a = b =

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Q: An equation is given. (Enter your answers as a comma-separated list. Let k be any integer. Round ter...

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Q: Compute the derivatives of the following functions. 1/x f(x) : x2 a. b. f(t) = 3/t g(t) = (1 – 3t)* ...

A: Hey, since there are multiple questions posted, we will answer first three question. If you want any...

Q: Use the power series 1 Iix:E(-1)^x^, \xl < 1 1 +x to find a power series for the function, centered ...

A: Given that the function, fx=arctanxSince,11+x=∑n=0∞-1nxn,  x&lt;1Therefore,11+x2=∑n=0∞-1nx2ntan-1x=∫...

Q: Find A, B, and C in the following partial fraction decomposition: A (x – 1)?(x – 3) X - 1 (x – 1)² x...

A: Given equation is : 2x-12x-3=Ax-1+Bx-12+Cx-3 Now 2x-12x-3=Ax-1+Bx-12+Cx-32x-12x-3=Ax-1x-3+Bx-3+Cx-12...

Q: How many points of inflection does the function f(x)=x8-x2 have?

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Q: A person starts walking from home and walks: 3 miles East 2 miles Southeast 5 miles South 5 miles So...

A: A person starts walking from home and walks:3 miles East2 miles Southeast5 miles South5 miles Southw...

Q: simplify as much as possible please

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Q: ∫1/x2√4+1/x dx, u=4+1/x

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Q: Given the triangle 14 find the length of side æ using the Law of Sines. Round your final 49° 17 answ...

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Q: Solve the rational inequality: (x + 4)/(2x - 1) ≤ 3and graph the solution set on a real number line....

A: Given rational inequality is x+42x-1≤3 Solution: Solving the given inequality, x+42x-1≤3x+42x-1-3≤0x...

Q: Find the Jacobian w/ respect to UVW X=U(3-v), Y= uv(3-w), Z=Uw

A: Our aim is to find the jacobian of x=u(3-v), y=uv(3-w) and z=uvw⇒x=3u-uv ,   y=3uv-uvw and z=uvwJaco...

Q: For the following vectors, (a) find the dot product v• w; (b) find the angle between v and w; (c) st...

A: Angle between the vectors is π , So both vectors are parallel with opposite direction. Explanation i...

Q: The rate of decomposition of radioactive radium is proportional to the amount present at any time. T...

A: The rate of decomposition is proportional to y, we know that y=Cekt, where t is the time in years. T...

Q: Find the exact length of the curve. y = In(sec(x)), 0<x< n/6

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Q: Rational Function, write the function for the graph given below. All intercepts are integers. Please...

A: From the given graph:   The function cut x-axis at x=-2 and x=1   Hence the x-intercept at x=-2, 1  ...

Q: Try it #2 Suppose that f(x)dx = 5, Só f(x)dx =-3, S g(x)dx = –1, and ſ g(x)dx = 2. Find the followin...

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Q: 5. Wallpaper was applied to one rectangular wall of a large room. The dimensions of the wall are sho...

A: Given that: The dimensions are 42 feet and 25.5 feet Since it is rectangular wall, the area of trian...

Q: Suppose parametric equations for the line segment between (2, 8) and (– 2, 0) have the for s ¤(t) = ...

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Q: How do I do this?

A: Given: gx=x2-9+lnx2+3x-4+e5x-2+4x+1x2-5x-1 we know that domain for x, lnx, fxgx is given by x≥0∩x&gt...

Q: What dp you mean by interpolation?

A: To define: interpolation.

Q: Determine whether the sequence converges or diverges. If its converges, find its limit {n3 / (n3 + 4...

A: Consider the given sequence, n3n3+4 Use the theorem which states that, if ∑an converges then limn→∞a...

Q: How do I solve this integral problem?

A: Given,          ∫x-322-xdx

Q: A rational function is given. r(x) =  4x + 1 x − 5 (a) Complete each table for the functi...

A: detailed solution and filled table is given below  

Q: 8. A quarterback throws a football with an angle of elevation 60degree and speed 60 ft/s. Find the h...

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Q: Without solving the equation x^2+2x-1=0 calculate the sum 1/x1+1/x2

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Q: Find f f"(x)=x-2  x greater than 0 f(1)=0 f(6)=0

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Q: Evaluate the integral below by interpreting it in terms of areas in the figure

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Q: Evaluate the integral. Check your results by differentiation. (Use C for the constant of integration...

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Q: sec 10.2

A: Given a=13cmb=5cmc=12cm

Q: Determine all critical points for the following function. f(x) =x-12x+3

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Q: 3rd question

A: This question (question 3) is based on the concept of logarithm and its properties. log7 (1/49)=x If...

Q: An equation is given. (Enter your answers as a comma-separated list. Let k be any integer. Round ter...

A: We know that, general solution for tanθ=tanα is given as θ=nπ+α ; n∈ℤ

Q: Use Simpson's rule with n = 6 to approximate (2)soɔ cos(z) -dz Preview Keep at least 2 decimal place...

A: Given ∫15cosxxn=6

Q: Use a calculator to solve the equation 3 cos2 x - 8 cos x - 3 = 0, correct to four decimal places, o...

A: We have the given equation as, 3cos2x-8cosx-3=0 On solving further, we get the result as 3cos2x-8cos...

Q: Suppose that f(-4)=3, f'(-4)=0, g(-4)=3, g'(-4) = 4. Use this to compute (f•g)'(-4)

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Q: Calculus Question

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Q: An equation is given. (Enter your answers as a comma-separated list. Let k be any integer. Round ter...

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Q: Use the power series for f(x) = arctan(x) to approximate the value, using Ry s 0.001. (Round your an...

A: Given that: arctan14