Write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as possible- variable expressions represent positive real numbers. OinO + %3D ロG

Q: You want to produce a cylindrical water container with a capacity of 350mL. What dimensions will…

A: We have to find the dimensions of the cylinder.

Q: 4. y = x, y = 2x, and x + y = 6 (Answer: 3 s. u.)

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Q: Ул4 — dx 2x2 + 1 3,

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Q: Find the general equation of the tangent plane to the surface x2 + y2 −2xy −x + 3yz = −4 at the…

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Q: Graph y = - cos (x -) by Transformation of y = cosx. Show and label each Trigonometric function…

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Q: b. dx Vr - 2x2 + 1

A: To evaluate: I=∫x5x4-2x2+13dx=12∫x22(x2)2-2x2+132xdx Substitute x2=u⇒2xdx=du

Q: 20 22. cot 3 - V3 -

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Q: Sketch the region bounded by the given lines and curves. Then express the region's area as an…

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Q: Select the correct answer. The graph of the function fx) = x3 defined over the interval [0, 1] on…

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Q: Integrate using any applicable method. Be sure to give an exact answer. (3z+1) Enter your answer in…

A: Solve the following

Q: 19. cos (20) 1/2

A: We will find the value of θ in the following step.

Q: Find the slope of the tangent line to the r=2-3cos 0 in polar coordinate at 0 =

A: Given:-r=2-3cosθdrdθ=3sinθTo convert from Polar Coordinates (r,θ) to Cartesian Coordinates (x,y)…

Q: Q3: Find the value of n which F(x, y, z) = (x +y +z*)" to satisfy fxx +fyy+ fz= 0. 1

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Q: Tangent to the curve z2 = 2xy + x² , z = 3 , at the point ( 1, 4 , 3

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Q: Find the absolute maximum and absolute minimum of the function f(x)=3sin(x)cos(x) over the interval…

A: We have to find the absolute maximum and absolute minimum of the function f(x) = 3 sin(x) cos(x)…

Q: b. d.x Vx4 – 2x2 + 1 3

A: Let's find.

Q: 2 | (csc 0)(1 + sin? 0 + sin 0 cot? 0) do

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Q: Solve the following initial value problem. f′′(x)=−36x^2−18x−4,f′(−1)=13,f(−1)=−35

A: To solve the initial value problem.

Q: Describe the end behavior of the graph of the function f (x) = 5(4)" - 10. For o, type in the word…

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Q: Determine the exact value of 2 sincos cos 12 12

A: Given query is to find the exact value of the expression.

Q: h(x) = (2x2 - 5x)2 / √3x-2 1. Explain how the function you chose can be rewritten in such a way…

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Q: A. Assimilation (Time Frame: Since we already presented S sin x dx and ſcos x dx, we can now do the…

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Q: Solve the following initial-value problem. f′(x)=2 3√x+3x^2, f(0)=6

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Q: Use the substitution u = 4x2 +1 to convert the integral fo ret+1 dx to an integral of the form Sº…

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Q: iv. L, x* (e* – e*) dx

A: Given:

Q: x² – 2x – 1 dx I ( – 1)²(x² + 1)

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Q: 1. Evaluate the following integrals. | (csc 0)(1 + sin² 0 + sin 0 cot? 0) de а.

A: Given ∫(cscθ)(1+sin2θ+sinθcot2θ) dθTo evaluate the integral:

Q: Find the net signed area between the graph of the function f(x) = |x+ 3| – 4 and the x-axis over the…

A: Here the area can be found by dividing the entire part in small triangles and adding the respective…

Q: dz dz and ду IV. Suppose z is a function of x and y, and tan Vy? + x² = z"e©y. Solve for

A: We have to Solve as per given conditions.

Q: Find the Taylor series generated by f at x=a. f(x) = 1/x2, a= 10

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Q: Find the differential dy: y = In(sec² ( 3"-2*+5)). Find the differential dy: y = In(sec? ( 3-2x+5…

A: We have to differentiate given function

Q: Given: points A (3, 1, 6), B (5, -1, -2), and C (1, -3, 2) 1. Show that A, B, and C form the…

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Q: sin(x²) ate lim 1+0- e2r – 2x – 1°

A: zero by zero form then apply L hospital rule

Q: 2. Error Analysis. Writing an exponential function from a graph. • Carefully indicate the errors you…

A: Given problem:-

Q: What type of critical point is located at x =-6, if ƒ '(x) = (x – 2)(x + 6)?

A: This question is based on application of derivative.

Q: Find all the second order partial derivatives of the given function. f(xy) =xy° +y¢* +5 O A. f = 2x,…

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Q: olve the equation. Write the solution set with the exact values given in terms of common or natur…

A: Given query is to find the value of y.

Q: Find the derivative of the function at Pn in the direction of A. f(x.y.z) = xy + yz + zx, Po(2, - 2,…

A: The  derivative of f at the given point is given below.

Q: I just want to confirm if my solution is right. Please check. If not, please correct me.

A: You have done a mistake which I have shown in step 3 of this solution. Kindly go through it.

Q: The power series representation of 1 f (x) = 5x +4 is: O 5 25 125 x+... 256 4 16 64 25 125 x++...…

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Q: 4 Which formula would be used to calculate the trapezoid approximation of L dx using five…

A: We have to use trapezoidal rule. Option B is correct.

Q: What are the two values of k closest to 1 - 4 for which S sin? (x +4) – cos² (x + 4) dæ has a value…

A: The solution is given in the next step.

Q: Jse any method to determine if the series converges or diverges. Give reasons or your answer. 9n 2…

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Q: need to find nth term, question is: Find a formula for the nth term of the sequence -1, 8, -27,…

A: Given query is to find nth term

Q: (a) Use the Second Derivative Test to find the local extreme values of the function f(x) = (x³ –…

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Q: lim X- Sin X X3

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Q: 3 2x hnd the f area o 2. the Sheded veg ien

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Q: describes the position of a particle moving along a coordinate line, where s is in feet and t is in…

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Q: evn+2 2+3 n=1

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Q: the derivative of the function at P0 in the direction of A ​f(x,y,z) = 9excos(yz)​, P0(0,0,0)​, A =…

A: Given query is to find direction derivative.