For vectors ū = (1,-5,2) and v = (3, 1,-4), calculate the following: a) ū• i b) the angle between ū andv, rounded to the nearest tenth of a degree.

Q: Problem 1. Draw a direction field for the given differential equation. By hand, sketch an approxi- m...

A: Solutionn is here

Q: Consider the region R bounded between y=x2-4x and y=-x2+2x  Set up an integral for the area of the r...

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Q: he differential equation (8 – r²)dr = %3D r² (1n (;) – = 0 cos cos = 0 (r+ 4) (in (;) –

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Q: Evaluate

A: Please refer to the image below

Q: -n ) Σe n=1 1 d) Σ+ 3 п n=1 8

A: C) Given that ∑n=1∞e-n By the integral test, ∫1∞e-x dx=limt→∞∫1te-x dx                              ...

Q: Water is poured into a conical container at the rate of 10cm³/sec. The cone points directly down, an...

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Q: Estimate the slope of a line tangent to the curve f(x) = -2x2 + 3x +5 at point P(1, f(1))by doing th...

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Q: -5x + cos (9x) – 1 Evaluate lim 2x Submit an exact answer.

A: To Evaluatelimx→0-5x+cos(9x)-12x  

Q: 3x lim The limit 2 x-2 (see graph) is

A: Here, to find the given limit: limx→2+3xx-2

Q: 1. Evaluate the following limits. 3x + 10 – 4 (a) lim 2--2- r2 – 4x + 4

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Q: For the next five questions, consider the following differential equation: ( + ry")dr + (5y - ry+ y'...

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Q: ak+1 If lim k→+∞ ak = 5, then ak diverges. k=1

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Q: If f(x,y,z) = z In(x²ycosz): then fz is

A: Here, the given function is: f(x,y,z)=z ln(x2ycos z) Using the properties of the natural logarithm: ...

Q: 1 dx x/1+ x6

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Q: Let us try to find where a function is increasing or decreasing given the  following.  1. f(x) = x3−...

A: To find the function is increasing or decreasing in the given interval.

Q: Determine (without solving the problem) an interval in which solution of the given initial value pro...

A: Follow next step

Q: The figure below shows contours of g(x, y) on the region R, with 3 < x < 9 and 2 < y < 8. 8 -1 6 1 2...

A: Let's find. 

Q: » [3] S Te dx > Vex [4] S(x- s(x + !)° dx >

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Q: Estimate f′(2) for f(x)=6^x. Be sure your answer is accurate to within 0.1 of the actual value

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Q: Given the: 7(t) = (cos (3t), 4t, sin (3t)) Find the folowing: show complete solution a. unit tangent...

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Q: Use the appropriate limit laws and theorems to determine the limit of the sequence. 2n2 + 9n + 5 an ...

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Q: What is the general solution to the differential equation 2e* cot(y) dx – (4 + e*) csc²)dy = 0 ? (4 ...

A: Here, the given DE is: 2excot(y)dx-(4+ex)csc2(y)dy=0

Q: a. As x approaches -1, f(x) approaches what value on the first table? On the second table? b. Do the...

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Q: Use any method to determine whether the series converge. 1 (a) E 'k² + 15k + 1 This series diverges....

A: To check the convergence of the given series.

Q: dy find dx t - 1 If y = t and æ = t+1 dy A. 2t(t + 1)2 dx В. dy = t(t+1)² dx dy 2t С. dx (t + 1)? dy...

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Q: V1+x3 dx [6] S (7) (ax2a (x2a+1)*dx x-2 ах2а (7] S

A: Given: (1)   ∫1+x33x-2dx (2)  ∫ax2ax2a+13xdx

Q: 2. Viola drives 170 meters up a hill that makes an angle of 6° with the horizontal. To the nearest t...

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Q: d²y 2. Find the second derivative of x? – 3xy? + y3 = 15 dx?

A: The given equation is; x2-3xy2+y3=15.

Q: Find the direction cosines of the vector v = (2, –4, 4) %3D

A: The given vector v→=2,-4,4

Q: Using the graph find the following: (6.5) a. lim f(x) e. lim f(x) X-4 (4.2) f. lim f(x) (2). (6.2) b...

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Q: 3 V1+x³ [6] S dx > x-2

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Q: x'e-2x dx 20 dx 2

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Q: 2x -dx e* +1 Evaluate the integral of A e*- In(e*+1) +e B '+ In (e* + 1) + c © e*+ In(e*+1) +c D In ...

A: Given problem:-

Q: 26 E(- 1)"2n - %3D n=0

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Q: dx Ve ve

A: Integration

Q: Determine whether the series converges. 00 Σ k=1 V7k – 1 O The series converges. O The series diverg...

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Q: X-1 2. Complete the following tables of values to investigate lim X→-1 x+1 f(x) f(x) - 1 -1 - 0.8 - ...

A: Complete table:           For (a), In both of that tables the value of f(x) when x approaches -1 i...

Q: Which of the following is the general solution to the differential equa · (x – /x² + y² )dy = 0 ? dx...

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Q: Find all the maximum and minimum points of f(x) = x4 – 8x2.

A: As we are not given any particular, we will take the help of the graph here.

Q: Determine the values of r for which the differential equation y" – 36y = 0 has solutions of the form...

A: We have to find the number of values of r which satisfies the equation.

Q: Find the derivative of: y=x^(7sin(x)). (x>0).

A: Multiplication rule of derivative is used.

Q: The graph of y = f(x) has a y – intercept of 3 and the tangent line at the point (x, y) has an x- in...

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Q: Find the inflection points of each of the given curve.  3y = x3 + 3x2 – 9x + 3

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Q: dy = ay + b whose dt Write down a differential equation of the form 3 as t → o. 4 solutions all appr...

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Q: INTEGRAL Evaluate the following: e 20do 10. ↑ 1+ 3e20

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Q: Coffee is draining from a conical filter into a cylindrical coffeepot at the rate of 9 in./ min. Com...

A: Given:Coffee is draining from a conical filter into a cylinde rcoffee pot at the rateof 9 in3/min.To...

Q: Find a number a so that the tangent lines to y= x° + 11x +x + 13 at x = a and at x = a+ 1 are parall...

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Q: For which values of x is the function below NOT continuous?

A: To find out the values of x at which the function is discontinuous.

Q: S (x +) dx 2 X.

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Q: Find the gradient of f (x,y,z) = e^(x+y) cos(z) + (y+1)tan^(-1) (x) at the pint (0,0, pi/6) Alternat...

A: The function is given by fx, y, z = ex+ycosz+y+1tan-1x The point is x, y, z = 0, 0, π6 To evaluate: ...