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Q: Factor and simplify : (x2 + 3)-2/3+ (x2 + 3)-5/3

A: We factor out the lower exponent.

Q: Find the equation of the line tangent to y = 2sin x at x = p>2. Graph the function and the tangen...

A: Given: Function y = 2sinx To Find: The equation of the tangent line at x = p Concept Used: The equa...

Q: a) Find values of a and b such that the following function is differentiable everywhere: xS-1 fax + ...

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Q: The first term is 3500, and the common difference is 15. Which term of the sequence is 2795?

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Q: Factor: x2 + 6x + 9

A: We multiply the leading coefficient 1 with the constant 9. So 9. Then we factor 9 so that the sum o...

Q: Use your graphing utility to graph each side of the equation log3(3x - 2) = 2 in the same viewing re...

A: We will graph using a graphing calculator.

Q: Computing the derivative of ƒ(x) = e−x

A: Given function is

Q: Integrals in spherical coordinates Evaluate the following integral in spherical coordinates.

A: Given that, Now we need to simplify the above integral, By using the formula of integration, ...

Q: A machinist is required to manufacture a circular metaldisk with area 100 cm2 .(a) What radius produ...

A: Let the radius = r cm So the area is =πr2 cm2 .

Q: Interpreting directional derivatives A function ƒ and a point P are given. Let θ correspond to the d...

A: Click to see the answer

Q: find the slope of the line tangent to thegraph of ƒ at P.b. Determine an equation of the tangent lin...

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Q: Let logb 2 = A and logb 3 = C. Write the expression logb √(3/16) in terms of A and C,

A: Given :

Q: Find the area of the region bounded by the graphs of the equations. y = 1 − x4, y = ...

A: We sketch the region using a graphing calculator.

Q: x2 - 4 Let f1x2 X - 2 a. Calculate f1x2 for each value of x in the following table. x² - 4 b. Make a...

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Q: Computing directional derivatives Compute the gradient of the following functions, evaluate it at th...

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Q: Solve the equation 2 cos2 x + 3 cos x + 1 = 0 on the interval [0, 2π).

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Q: Add or subtract as indicated and write the result in standard form: 15i - (12 - 11i)

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Q: Differentiate the function. g(x) =x Sin(2x)

A: We will use the product rule

Q: 0 Find polar coordinates (r, ) af the point, mhare >0 and ose2r. ) Find polar caordinats (r, ) of th...

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Q: Using: limx→4f(x)=3 and limx→4g(x)=7, evaluate the limits, limx→4 f(x)g(x)= limx→4 f(x)/g(x)=

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Q: Find the formula for the volume of the region outside the smaller rectangular solid and inside the l...

A: The volume of the outer cube is = (a)(a)(3a)=3a3 The volume of the inner cube= (b)(b)(3a)=3ab2

Q: Let f(x) = 2x - 5. g(x) = 4x - 1, h(x) = x2 + x + 2. Evaluate the function g(f[h(1)]) without findin...

A: We plug x=1 in h(x) first

Q: Find a unit vector in the direction of the given vector. v=(-6,6)

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Q: Express the function,h(x) =1/(2x - 3) as a composition of two functions f and g so that h(x) = (f ∘ ...

A: We will take the inner function as g(x) and the outer function as f(x). Note that 2x-3 is inside. An...

Q: 4 Find the derivative ofƒ(x) = 4ex - 3x2

A: Differentiate both sides with respect to x.

Q: Determine the domain of the function and prove that it is continuous on its domain using Theorems 1-...

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Q: A continuous random variable X has probability density function {(5 – x) for 0 <x< 2 f(x) = otherwis...

A: Given probability density function for a random variable X is,

Q: Use the figures to find the exact value of the trigonometric function 2sin θ/2 cos θ/2

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Q: Find the union of the sets. {0, 1, 3, 5} ∪ {2, 4, 6}

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Q: Use the definitions of the hyperbolic functions to find each of thefollowing limits. limx→∞tanh x

A: We use the hyperbolic definition of tanh(x)

Q: Use the attached graph to a. determine the x-intercepts, if any; b. determine the y-intercepts, if a...

A: a) The graph cuts/touches the x-axis at x=-2 and x=1 So, x intercepts are x=-2 and 1 Answer(a): ...

Q: Integer coefficients Show that the first five nonzero coefficients of the Taylor series (binomial se...

A: .

Q: Find the derivativeof ƒ(x) = x5. Then find the samederivative using the Quotient Rulewith ƒ(x) = x8/...

A: Given: We have to find the derivative of f(x)

Q: What is the value of lim ? A-) B-) C-) 00 -1 D-)

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Q: Find cos 0 if cot 0 =4/3 and sin 0 < 0.

A: Also given that sinθ<0, this means sinθ is negative. So, cotθ=cosθ/sinθ means cosθ also have to b...

Q: graph the points z = x + iy that satisfy the givenconditions. | z + 1| = | z - 1 |

A: It is given that With the condition Substitute the value of z in (2)

Q: Solve absolute value inequality : 5 l2x + 1l - 3 ≥ 9

A: First we solve for |2x+1|

Q: Evaluate the definite integral.

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Q: Triple integrals Use a change of variables to evaluate the following integral.

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Q: Find the limit limx→π/2(sinx)tanx.

A: We use tan(x)=sin(x)/cos(x)

Q: Please solve the below given equation

A:

Q: (a) Show that the series $\sum_{n=1}^{n} \frac{n^{n}}{(2 n) !}$ is convergent.

A: Given As,

Q: Find a parametrization of the hyperboloid of two sheets (z2/c2) - (x2/a2) - (y2/b2) = 1.

A:

Q: Let f(1) = 2. lim7(x)-v2 = V2 and g(x)=arctan(xf(x)) . Then g'(1) =? x-1 1 2 3 3

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Q: Compute the discriminant of 4x2 - 8x + 1 = 0. What does the discriminantindicate about the number an...

A: The discriminant of 4x2 - 8x + 1 = 0 is:

Q: Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of...

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Q: Identify which graphs are not those of polynomial functions.

A: The given graph is of a parabola. We know that the equation of a parabola is a quadratic function. ...

Q: 3. Consider 3x3 matrix A the 1 A て 1. レ Colculate the adjoint matrix

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Q: Improper integrals Evaluate the following integrals or state that they diverge.

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Q: Find the standard form of the equation of the hyperbola with the given characteristics Center: (0, 0...

A: Given that the center=(h,k)=(0,0) a=Distance between center and vertex= distance between (0,0) and (...

Transcribed Image Text

x² – 10x – 5 dx |x- 1)-(x² + 1)