Condense the expression to the logarithm of a single quantity. (log3(x - + 1) + 2 log3(x – 1)] + 6 log3 x 2 log 2(4² – 1)(x –1)³ 12( 2 -

Q: Use the Root Test to determine the convergence or divergence of the series. (If you need to use co…

A: Given query is to find the series converges or diverges.

Q: Use the chain rule to find the derivative of: cos(7 + 8x)

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Q: Let h(x) = tan (2x + 6). Then h'(2) is and h'(2) is

A: topic- functions and derivatives

Q: Determina the vector field of F. F(1, y) = yi -j

A: Please see the below picture for solution.

Q: -2

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Q: 3 10. S 2x Vx2 – 3x + 1

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Q: SxV9-2x2 dx god Find .000.8S

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Q: e equation (2 cose – 1)(3 + tane) = 0 over the interval [0, 27]. solving for trig functions,…

A: We will solve the equation.

Q: Find the area of the region bounded by the graphs of the equations. y = -x2 + 6x, y = 0

A: Solution 1.  Given y=-x²+6x  And y=0 Now intersection point -x²+6x=0 X(6-x)=0 X=0 and x=6 Points…

Q: In ASTR, t = 15 ft, r = 16 ft, mLS = 35°. Find the area of the triangle and round to the nearest…

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Q: (2, 4) y = 2x ng a vertical element of area, he area of the shased region is gven by the integral

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Q: 1. sin 0 =

A: answer is in next step

Q: 12 Let y24xー4x+3 le) Find the eauetion.of the tangent Iine to the graph of the fuuction att x-2; O…

A: We have to find tangent line

Q: lim sec x x-(-71/2)"

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Q: Find curl (4z i + 5x j+ 3y k).

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Q: Consider F and C below. F(x, y, z) = (y²z + 2xz2)i + 2xyzj + (xy² + 2x²z) k, C: x = Vt, y =t + 8, z…

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Q: a. 0 =-45 → graph type = b. r= 8-8cos0 graph type = facing up/down/left/right? loop length = c. r=…

A: (a) θ=-45°Graph type straight linesymmetry along first and third quadrant     (b) r=8-8cosθgraph…

Q: 3 (a) | (7)dx (c) dx (sin x + 1)dx (b) L (x° + 2x + 1)dx (d) 0,

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Q: 1. Find the area of the region bounded by the given curves. Show the computed areas of sections…

A: Area bounded by the curves :   If f(x) and g(x) are two continuous function on a,b and f(x)≥g(x) on…

Q: A farmer finds that if she plants 90 trees per acre, each tree will yield 30 bushels of fruit. She…

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Q: The probability that an event will happen is . What is the probability that the event will not…

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Q: Given the function g(x) = 4x° – 36x?+ 96x, find the first derivative, g'(x). g'(x) = (x),6 Notice…

A: Given that, the function is g(x) = 4x³ - 36x² + 96x We have to find the g'(x),g"(x) and have to…

Q: Determine whether the series converges absolutely or conditionally, or diverges. (-1)" + 1 n + 8 n =…

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Q: dy a) If all of y = 4n2 + 5n + 1,x 3n + 2 find dx b) if yx2+Vx + xy? = 1 prove that = -at (1,-1)

A: Please see the answer below.

Q: FOLLOW

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Q: 2n+3 {a,} = 7n- 2 7n+4)

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Q: Ay (2, 4) y = 2x y = x2 2. Using a vertical element of area, the area of the shaded region is given…

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Q: Determine the area of the glven reglon. y = x + sin x 3- 2- Step 1 Note that for the given reglon, x…

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Q: A job applicant estimates that his chance of passing a qualifying examination is , and his chance of…

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Q: Find the tangent plane to the equation z 2y cos(5x – 4y) at the point (4,5, 10)

A: Given; z=2ycos(5x-4y) at the point (4,5,10)

Q: Find 17. d Ssin (4x) cos(4x) dx

A: Use substitution to solve

Q: and y=x+2 Revolve the area about the x-axis. Using circular ring method, the volume of the solid…

A: Given :-region bounded by y=x2  ,  y=x+2revolving about the x-axisusing washer/disk…

Q: Write the first four terms of {an}. n + 1 10) an 3n - 1

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Q: 24) Identifa tue internel of convergen ce of a power ser's Ž (3)" n-1 (-3)", n=) a ) b) c) d) 3 2x23…

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Q: 16 Indicate the general rule for the arithmetic sequence with a3 = 8 and a8 = 33. a n = 2 + (n -…

A: The nth term of an arithmetic sequence is an = a + (n - 1)d  a is the first term. d is the common…

Q: Fit a second degree parabola y = ax² + bx + c to the following data %3D 3. y 1.8 1.3 2.5 6.3

A: Normal equations associated with y=ax2+bx+c are: ∑y = a∑x2+b∑x+nc ∑xy=a∑x3+b∑x2+c∑x…

Q: Find the standard form of the equation of the hyperbola with the given characteristics vertices: (-…

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Q: F(x) = dt Step 1 Rewrite the glven functlon F(x) D, -2 dt as F(x) =D -2t dt.

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Q: 15x + 44 -5x + 84=26 then astructions: Rewrite each Systems of equatons as amatrix, perform cow…

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Q: petdo eidj to noitom paidi b noit t no eog edt bnt Use the limit process to find the area of the…

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Q: 9) use the snell metnod to sef up end eveluete tueinteyrel tret gives the volume of the solid…

A: Using shell method, volume is evaluated.

Q: Find (3+2)-2i. 406 754 386

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Q: 3. If f(x) = [ 8+f dt ,find f'(1). .

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Q: The area bounded by y=3Vx and 2y =3x is revolved about the y-axis. Using circular ring method, set…

A: This question can be solved using the concept of circular ring method.

Q: 8. Given the following information, sketch a continuous graph of r(x) as accurately as you can on…

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Q: Evaluate the definite integral. Use a graphing utility to verify yourr result. (sin(x) – 3) dx Step…

A: To evaluate the given difinite integral. By using a graphing utility to verify your result.∫0πsinx-3…

Q: -12 1. ("(25x – 46x + 3)dx -12

A: topic- definite integral if f(x) is a odd function∫-aaf(x)=0

Q: Evaluate the following definite integral.  4

A: topic- definite integral

Q: Use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is…

A: To determine whether the given series is convergent or not.

Q: The equation of the ellipse that has its center at the origin with focus at (0, 4) and vertex at (0,…

A: The ellipse has its center at the origin with focus at 0,4 and vertex at 0,7