Given the definitions of f(x) and g(x) below, find the value of (fog)(-1). f(x)= x +5 g(x) = 2x² + 4x + 13

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Q: For the following exercises, use the Mean Value Theorem and find all points 0 < c < 2 such that ƒ(2)…

A: The given function is,Take derivative.Substitute x=c

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A: To find the line integral of a scalar field f(x,y) over a curve C, the general formula is:Segra…

Q: 2x 1) Calculate the derivative of h(x) = √√e²x +e-²x

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A: 2 cos(theta) = - sqrt(2), [0,2 pi)

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Q: The function s= -1³ 31²-31, 0sts 4, gives the position of a body moving on a coordinate line, with s…

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Q: 8. An engineer invests $27,000 in two bonds. If one 7% and the other yields 9%, how much is invested…

A: Let engineer invest $x on one bond which yields and  on another bond which yields

Q: Find a formula for the general term an of the sequence assuming the pattern of the first few terms…

A: To find a formula for the general term  of the following sequence.

Q: Find the volume of the solid obtained by rotating the region bounded by the x-axis, the y-axis, the…

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Q: √ 5x(x² +4)√√x² + 4 dx. 2

A: To evaluate the following integral.

Q: 8. Let f(x) = sinx, g(x) = cos x. The functions f and g, considered on the interval [0, π/2], are…

A: The given functions are the inner product of two functions f and g on the interval [a, b] is the…

Q: Let h(u) = (u +3) (u - 4) Determine the most general antiderivative of h. (u +3)(u — 4)du = -

A: Given,

Q: Find the integral. Use C for the constant of integration. | (x² (y² + 3)² dy

A: The objective of the question is to find the integral of the given function with respect to y. The…

Q: Compute the curl ∇ ✕ F of the vector field. F =

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Q: Find the volume of the solid obtained by rotating the region bounded by y = x, the line x = 4 and…

A: To find the volume of the solid obtained by rotating the region bounded by , the line  and the…

Q: Find the cost function for the marginal cost function. C'(x) = 0.07e0.05x; fixed cost is $7 C(x) =

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Q: 1 7. Ση=0 (2n+1)!

A: The given series is

Q: Evaluate ff xdxdy where R is the region bounded by x=2, y = 0 and y = x

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Q: Consider the following integral. √1 + 7x dx Find a substitution to rewrite the integrand as du. u¹/3…

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Q: g. y = ex² +1 h. y = esinx y = ln(sin x) i. j. y = ln² + e√x X 6. L

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Q: 3. Consider the function y = f(x) whose curve is given by the equation 2y² - 6 = y sin x for y > 0.…

A: Note:-As per your demand we solve part d for you Given derivative and point when is

Q: k. y = ln x 1. m. y = y = 5 cos x + 8 lnx + 3x³ 3x¹+3x²+1 x

A: Given: y= ln(x)Solution: y= ln(x)Differentiating y with respect to x we have dydx= ddx(ln(x)) ⇒y′=1x

Q: 3. The behavior of the system is a spiral source. x' = y' = = 3x + y, -x + 4y

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Q: Consider the parametric curve: x Y 4 +² +³4t At which t value(s) is the tangent to this curve…

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Q: Suppose you are given a triangle with Then a = , and b= 9. Enter your answers with at least 3 digits…

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Q: The function y(x) saifies the following equation: Find an expression for dy dx 5 x² − 2xy+3y² − 3 x…

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Q: 2. Σ. 1 (-5) 2n n2gn

A: The given series is The Root test If L&lt;1 then series is absolutely convergent If L&gt;1 then…

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A: Given that, the function is .We need to find the value of x for which the given function has a…

Q: 2. The behavior of the system is a saddle. y' = -x + y, = -x-y

A: Given system is x' = -x +yy' = -x -y

Q: Find the area under the curve y = 9x5 over the interval [0, 2]

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Q: Find the mass of a lamina bounded by y=5√x,x=9,and y=0 with the density function σ(x,y)=x+1

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Q: 8. Find the linearization L(x) of f(x)=√√x² +9 at x = -4.

A: Given that the function

Q: 4. Find the derivative of the following functions: a. y = x² sin x b. y = ex cos x 3 c. y = (x² + 1)…

A: *Note – As per our company guidelines we are supposed to answer only first 3 sub-parts. Kindly…

Q: 2. Evaluate the integrals. a. b. C. L (6x - e²) dx [²₁12 +2 (2 + 2y)² dy 7T/4 3 3 sec Ꮎ tan Ꮎ ᏧᎾ

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Q: Use chain rule to find the derivative of the following functions: a. y = sin(5x) b. y = cos(x²) c. y…

A: We have to find the derivative of the following functions by using the chain rule.Chain Rule: In…

Q: A physician invests $24,000 in two bonds. If one bond yields 6% and the other yields 12%, how much…

A: Given that a physician invests 24000 dollars in two bonds , 6% and 12% , total annual income 1980…

Q: (3√2, -3√2,6) to cylindrical to cylindrical coordinates. Enter your answer as an ordered triple and…

A: Cartesian coordinates:(x,y,z)=(3√2,-3√2,6)

Q: Find a simplified series representation of x²e4 answer = n

A: The given function is x2e4x.

Q: 3 · [²³ F(x) Given 6 ³ fº f(x) f(x) dx = 9 and Exercise (a) 6 [° F(x) f(x) dx = -8, evaluate the…

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Q: Find a power series representation for the function. ( ) = n( 11 + y )

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Q: Find the derivative of the function. y = ³√x²-x² 一 y' =

A: The given function is; y= x7/8

Q: Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an…

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Q: (3, 7/7). 2 Plot the point whose polar coordinates are (3,

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Q: 6. 14 ) Consider both geometric series below. 3 SA = 00 Σ n=1 5n and SB = M8 n=0 3 5n Both SA and SB…

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Q: The approximate rate of change in the number of design patent applications received in recent years…

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Q: Find the limit of the sequence an = (cos.n) 5"

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Q: Find ∫∫R(5x+2y)dAwhere R is the parallelogram with vertices (0,0), (-2,3), (5,-4), and (3,-1). Use…

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Q: Find a vector function, r(t), that represents the curve of intersection of the two surfaces. The…

A: Trigonometric function can be used as parameterization of many curves, this is thanks to the use of…

Q: For timer 20, the function Cate with positive constants a and b gives the concentration, C, of a…

A: The given function is