Consider the function f(x)=x^5 - 5x^4 a. Find where the function is increasing and decreasing.   b. List any relative extrema as ordered pairs. Label as max/min

Q: 7-38 Evaluate the integral. 7. X - 1 dx 5x + 1 9. dx (2x + 1)(x – 1) 11 dr

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A: Given Series ∑k=1∞-27k

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A: Here we have, The length of a rectangle is increasing at a rate of 2 ft/s, and its width is increasi...

Q: | cos(Tx)|+ x2 I a+1 + 5x + 137 (9) Find all a so that dr converges. You do not have to find the val...

A: We shall use the limit comparison test to answer this question.

Q: Find the arc length of the graph of the function f(x) : In(sin(x)) over the interval 11 7

A: Let's find. 

Q: 27. y (2, 12) 3

A: As per our guidelines we are supposed to answer only one question.kindly repost others question as a...

Q: du Formula Answer 7. S 4-5x+1 dx

A: Given: I=∫5x4-5x+1dx   .....(1)   We know that; The chain rule: fgx'=f'gx·g'x The derivative of ax i...

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Q: Using variable separable technique, find the general solution of (4x+xy^2)dx + (y+x^2y)dy = 0

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Q: 9. An amount of $12, 000 is deposited in a bank that pays interest at a rate of 3.5%, compounded con...

A: Given :Total Deposited amount = $12,000Rate = 3.5%Time = 4 years

Q: Find the minimum and maximum values of the function f(x, y, z) = x² – yº – z® subject to the constra...

A: We have to find the minimum and maximum values.

Q: Find the derivative as indicated: 1) y = 3 cos x +2 sin x; find y' 2) f (t)-t sin t find f' ()

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Q: 1. tanosin20 = 4tan0 %3D

A: Since you have asked multiple question, we will solve the first question for you as per our guide li...

Q: 4. y = sin(cos 3x) – sin x cos 3x |

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Q: Find dy/dx 1. y= cos ( -2x -10) 2. y= cos³ -5x

A: We have to find derivative dy/dx.  

Q: 16. Suppose that over a region of space the electrical potential V is given by V(x, y, z) = 5x² – 3x...

A: We have to find direction in which V change the most rapidly at P and maximum rate of change at P. W...

Q: The altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is inc...

A: The altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is inc...

Q: Use the Comparison Theorem to de x + 1 36 dx Ji O convergent O divergent 8

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Q: Given the general solution to a differential equation and its initial conditions y(t) = C,14 + C,-2 ...

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Q: (8) Find all k so that aek= dx converges. In this case, find the value.

A: Given problem:-

Q: 2. An iPhone 13 pro max is dropped from the top of the Balayong Park monument, 225 ft high. (a) How ...

A: This question can be solved by using the equations of motion.

Q: 1. lim f(x) = -1 and f(1)DNE 2. lim f(x) 1 and f(0) = -3 x-1 3. lim f(x) = –2, 4. lim f(x) = +∞, x-2...

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Q: Given the differential equation y" - 4y' + 13y = 8 e2* cos(3x) Determine the General Particular Solu...

A: Given differential equation, y''-4y'+13y=8e2xcos(3x)  

Q: 3. (a) P - 3e + 2x 32

A: By our policy, we are allowed to solve only one question at a time. Kindly repost the other question...

Q: cos" (coxx)

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Q: Inverse Laplace Transform; f(s)= 1/s-3

A: Laplace Inverse Transform of 1s-3

Q: Зх +7 -dx = (х—1)(х-9)

A: Fully evaluate the integral.

Q: b) fx*/25x² – 4cx -4dx

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Q: Evaluate the integral. (Use C for the constant of integration.) dx x² + 9 2+9 n(x+ Vx² + 9 ) +C ×

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Q: Find the minimum and maximum values of the function f(x, y, z) = 5x + 6y + 4z subject to the constra...

A: Here we have f(x,y,z)=5x+6y+4z subject to the constraint x2+6y2+6z2=1 Let g(x,y,z)=x2+6y2+6z2-1

Q: For the next three questions, consider the following differential equation: (2y sin r cos r-y + 2y²e...

A: Find your answer below 

Q: 12. cosx(1+ tanx)² = secx + 2sinx %3D

A: Prove : cosx ( 1 + tanx)^2 = secx + 2 sinx

Q: Find y ′ and y″ by implicit differentiation. x2 + xy + y2 = 5 y ′ = y ″ =

A: We have to find  y ′ and y″.  Given x2 + xy + y2 = 5

Q: 1. S dx x³+2x x2+1

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Q: x-intercept  (x,y)=           (smaller x-value)

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Q: Q2) if the vechrs V=-i +5 and ū=Tz i+5J+2 R Find a) The scalev component of ū in the divection of V ...

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Q: Use Lagrange multipliers to find the maximum area S of a rectangle inscribed in the ellipse 25 = 1 (...

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Q: Determine whether the series converges, and if so find its sum. 4k+2 2 7k-1 k=1

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Q: COSX cosx 10. 1-sinx 1+sinx

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Q: 5. Calculate the derivative of f(x) Use this result to determine whether the sequence x2 + 1 n An = ...

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Q: cate whether lim f (x) and f(c) are equal or unequal at th ate whether lim f (x) or f(c) does not ex...

A: In this question we will use basic concepts of calculus i.e concept of limits. Solution of the above...

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Q: (sec A - 2)(2 csc A - 1) = 0. What quadrant does A terminate? A. IV only B. II & II C. I & IV D. I o...

A: The given equation is  sec A-22csc A-1=0

Q: 2. Determine whether the statement is true or false. [3, xs2] l0, x>2/, then lim f(x)=3. a. If f(x)=...

A: f(x)=3x≤20x>2  

Q: Use any method to determine whether the series converge. (a) k=1 12k The series 1 (b) 2 12* + 1 k=1 ...

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Q: Find the lines that are tangent and normal to the curve at the given point. x²y? = 36, (1,6) %3D

A: We will find first slope of tangent and then from the slop and tangent and point will find a equatio...

Q: Q3) If P(2,-2, 1) , Q(3,-1,2) and R( 3,-1,1) ノ の)ind the area of the triangle determined by the Poin...

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Q: Find all local maxima, local minima, and saddle points for the function: f(x, y) = x – 6xy + 8y

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Q: Find the following limit value. Show all work and proper limit notation. 9х + бх2 — 8х5 lim 3x2 + 8x...

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Q: Hw. Fimd ow and dw for the following functions 3 2 we cosh (cot() 3- 4-

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