Find the first derivative of y = ( ex – e –x ) / (ex + e –x ) and y = ln [ x + √ (x2 + 1) ] Simplify the answer. Make the solution detailed and clear.

Q: A manufacturer needs to make a cylindrical can that will hold 1.5 liters of liquid. Determine the…

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Q: the product z1 z2 in polar form? Z1 = 3 cis z2 = 4 cis - cis (금) cis () 7x 2 cis ()

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Q: When 20 N of force is applied to a spring of natural length 2 m, the resulting compression is 0.5 m.…

A: Natural length = 2 x1=2-1.5=0.5x2=2-1=1

Q: 7) Assume that the temperature of a person during an illness is given by: T(t) = t2 +1 5t + 98.6, in…

A: topic - derivative of a function

Q: 12 and x terminates in quadrant IV. 5 Find sin 2x, cos 2x, and tan 2x if tan x= sin 2x cos 2x tan 2x…

A: To find sin2x, cos2x and tan2x for the given value of tanx .

Q: 1. For the right triangle pictured below, find the exact values of each of the following (no…

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Q: Supply the missing integrand and the limits of integration n/2 2sin e r cos?e dr de = | _de 2sin e…

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Q: Question Ris the region bounded by the functions f(x) = /3x - 1 and %3D g(x) = +2. Find the area A…

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Q: sec x lim X0 InX

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Q: Find the volume of solid generated by revolving the area enclosed by: x = y2 + 1, x=0, y=0 and y=2…

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Q: 9. Find f x • e*dx as a power series. (You can use e* = E=o 100

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Q: Find the area of the following shape, 212 2/2 9/2

A: We have to find the area of the given shape

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Q: Complete the proof of the identity by choosing the Rule that justifies each step. sin'x+ 3 cos?x=1+2…

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Q: What is the derivative of x sin(x) at the point (6,5)? 2 O 1 O-1 O None of the above

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Q: 14. Write an expression that gives the area under the curve as a limit. Use right endpoints. Curve:…

A: The area under the curve fx=x2 from x=0 to x=1.

Q: If f(x, y) = e“ sin(4y) then: 4 sin (4) 4 cos( 4) V f( – 1, 1) . el el

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Q: 8 Given a function: f(x) (х-7)(х-1) Write down the definition that lim f(x) = L = 1| 8 oProve that…

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Q: The auxiliary roots of the auxiliary equation associated with a certain HLDE are m=±3, ±3i, + 3i.…

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Q: ) Find extreme values of f(x, y, z) = x^2 + y^2 + z^2 subjected to the constraint x + 2y + 2z = 12…

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Q: Write in logarithmic form. 45/2 = 32 log 232 O A. = 4 log 54 5 O B. log 432 = 5 Oc. log 54 = 2 5 O…

A: We want to write the given expression in logrithmic form.

Q: Find the Rlemann sum for f(x) = x +3x over the Interval [0, 8] (see figure), where %3D X, = 0, x, =…

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Q: Use the properties of limits to help decide whether the limit exists. If the limit exists, find its…

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Q: Calculate the following limit: lim( lim(3) e-5z+6 2-9 O 1/6 0 1 O does not exist

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Q: (24) Evaluate the integral: / Va sin(1+ x/²)dx. (25) Find the equation of the normal line to the…

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Q: 9) y = e4x² + x A) dy dx 8xe2x + 1 B) dy - 8xex2 dx %3D + 1 C) dy dy - 8xe4x2 dx — 8хе + 1 %D D) + 1

A: We have to find

Q: : The vectors a and b span R°. What values of m and n will make the following statement true: (2m +…

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Q: d (32) Find the derivative: dx rcos(r) V1- t?dt

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Q: 15. The graph of f(x) is shown below. Use it to evaluate S(x)dx Area7 Area4

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Q: Using the method of undetermined coefficients, what is the modif ied form for a particular solution…

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Q: Find all solutions of the equation in the interval 0, 2n). 3 sin 0+1= 1 Write your answer in radians…

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Q: Find a vector that is perpendicular to the given vectors. 3) i = (-5, 6, 7) v = 1, -9, 0) 4) RS and…

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Q: 25n Evaluating sec will yield to 6 V3 A 2 2/3 B 3/3 © - 2 V3 D 2.

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Q: What is the derivative of sin(2x) at the point (0,0)? O 2 O -2 O 4

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Q: V1-x² dy dx |-V1-x²

A: Solution: ∫-11∫-1-x21-x2 1·dydx

Q: lim X→1 X-1 Inx

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Q: Supply the missing integrand and the limits of integration dx dy -L- _dy ху A I (e-1)dy -1 y e'dy dy…

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Q: (D² +4)y = 4cos x

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Q: Find f/(x). If f(x) = tan-1x? .2 %3!

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Q: Using the method of undetermined coefficients, what is the modified form for a particular solution y…

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Q: Find the radius of convergenee and interval of convergence for the following. (x – 2)" 2 2" (2n)!…

A: The given series,       ∑n=1∞x-2n2n2n!

Q: Find dy/dx by implicit differentiation. 12Vxy +4xyVxy –y dy/dx %D x – 2x²Vxy

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Q: Write an equation for a rational function with: Vertical asymptotes at x = 3 and x = 1 x intercepts…

A: We have to find the function

Q: Let f(x) =- 9x2 Determine the intervals on which f is increasing and decreasing.

A: Given: f(x)=x44-2x3+9x22 To find out if a function is increasing or decreasing, we need to find if…

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Q: Complete the table and use the result to estimate the limit. Use a graphing utility to graph the…

A: Here we have to find the value the limit of the given function using table values.

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A: equation of circle

Q: Write an equation for the polynomial graphed below 5+ 4+ 3- -2- -3 -4 -5+ y(x) %3D 2)

A: topic- polynomials

Q: Let f (x) =: 5 +e'+ tanx+ 12*+Vx. Find f (x). For the toolbar, preco

A: On solving this we will get

Q: A city had a population of 2,238 at the begining of 1965 and has been growing at 9.6% per year since…

A: TOPIC- EXPONENTIAL FUNCTION