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Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the uni...

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Q: Find the degree 2 Taylor polynomial of f(x): at a = 0. x +2

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Q: 5. 8- 4. h(x) 7- g(x) 5. 4- 3. 3 x-values 4 4 x-values g(x) h(x) If f(x) then f'(1) - 3. 2. 3. N tou...

A: From the graph g(1)=7 and h(1)=3 g'(1)= slope of g(x) at x=1 is = -2 [because 2 units down for 1 u...

Q: Use the given vectors v = 3i + j, w = i + 3j to find v.w and v.v

A: Given:v=3i+jw=i+3jv=3 , 1 w=1 , 3Dot product:a→.b→=a1b1+a2b2i→.i→=k→.k→=j→.j→=1

Q: Fill in the blank/s : We can rationalize the numerator of [√(x + 7) - √x] / 7 by multiplying the num...

A: To rationalize the numerator of x+7-x7

Q: Q3.5.Ellis Autotrol, Inc. plans to install an ecofriendly energy recovery system that will cost an e...

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Q: 13. How many inflection points can a:(a) quadratic polynomial have?(b) cubic polynomial have?(c) pol...

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Q: Evaluate the geometric series or state that it diverges.

A: ∑k=0∞(14)k sum of GP = a1 - r a is First term and r is common ratio when k = 0 ---> a = (14)...

Q: A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus the diameter of the s...

A: Width of rectangle = x ft Diameter of circle = x Radius = x/2 Circumference of semi-circle = π×r=πx...

Q: Please show work on how to get the answers

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Q: 1-tan x 1+ tan x sec x-CsC X a. sin x + cos x sin x COS X b. sin x +cosX sin x + cos X C. sin x- cos...

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Q: The first part of a is right but I keep getting the second part of a wrong. Also need help with part...

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Q: Water is flowing at the rate of50 m3/min from a shallow concrete conical reservoir (vertexdown) of b...

A: Given that, water is flowing at the rate of 50 m3/min from a shallow concrete conical reservoir (ver...

Q: Evaluate the global maximum and global minimum of the function g(x) = 8 √( x – 4) defined over the i...

A: The given function is gx=8x-4 in the interval 4≤x≤29. First find the derivative of the function, gx...

Q: A right angled triangle is to be constructed so that the hypotenuse is 20cm long . The height of the...

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Q: find a linearization at a suitably chosen integer neara at which the given function and its derivati...

A: Given f(x)=sin-1x , a=π12

Q: 9. sin75°cos15° + sini5°cos75°

A: As you have not mention which question to solve and we are allowed to solve one doubt in a session, ...

Q: a) Find the center-radius form of the equation of the circle with center (0,0) and radius 7. b) Grap...

A: Givencenter of the circle=(0,0)radius=7

Q: (a) Find [F(t) • G(t)] (b) Given p(t) = 3VE , evaluate [p(t)F(t)] dt

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Q: Evaluate the integral, if it exists.

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Q: Fill in the blank/s: To convert a complex number from rectangular form, z = a + bi, to polar form, z...

A: we know that a+ib=rcosθ+isinθ where, r=a2+b2, tanθ=ba

Q: find lim x-> 0, cos (12x)-1 / 3x

A: Given, limx→0cos 12x - 13x Move the term 1/3 outside of the limit because it is constan...

Q: Calculus Question

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Q: Find the degree 2 Taylor polynomial of f(x) = In(x + 1) %3D at a = 1

A: The Taylor polynomial about 1 of degree 2 is given by: T2(x)=f(1)+f'(1)(x-1)+f"(1)2!(x-1)2

Q: It's not option A

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Q: 2 questions in Pre-Calculus

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Q: Use the four-step procedure for solving variation problems to solve: Body-mass index, or BMI, takes ...

A: Given BMI varies directly as one’s weight, in pounds, and inversely as the square of one’she...

Q: Find the derivative of ƒ(x, y) = xey + cos (xy) at the point (2, 0) in the direction of v = 3i - 4j.

A: Given: f(x,y)=xey+cos(xy) at point (2,0) in the diection of v=3i−4j

Q: Fill in the blanks: The goal of an optimization problem is to findthe maximum or minimum value of th...

A: Given information: The goal of an optimization problem is to find the maximum or minimum value of th...

Q: Simplify the given expression. cot (sin (A)) =

A: To simplify the expression cotsin-1A Let sin-1A=yA=siny=PerpendicularHypotenuseBase=H2-P2=1-A2coty...

Q: Sketch the solid described by the given inequalities. 0 <= theta <= pie/2, r <= z <=2

A: r≤z≤2, 0≤θ≤π2 We need to sketch the solid.

Q: Identify the surface whose equation is given.

A: ρ cos Φ =1 -> z = 1 ( as we know in spherical coordinates z = ρ cosΦ)

Q: setup dxdydz only

A: Given: ∭Bx2+y2+z2dV, whereB=x,y,z:0≤x≤4, 0≤y≤4, 0≤z≤4 To Setup: dxdydz

Q: Setup cylindrical only

A: E is the region that lies inside the cylinder x2+y2=16 and between the planes z=-5 and z=4 Change th...

Q: Use the exponential function f(x) = 42.2(1.56)x to find the average amount spent, to the nearest dol...

A: Consider the following exponential function: fx=42.2×1.56x where, fx=Average amount spent in x hours...

Q: Determine if true or false and provide an explanation to support my answer.

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Q: Principal unit normal vector Find the unit tangent vector T and the principal unit normal vector N f...

A: Unit tangent vector: T(t)=r'(t)r'(t) Unit normal vector: N(t)=T'(t)T'(t)

Q: Find the slope of the line passing through pair of points (-2, 4) and (-1, -1) or state that the slo...

A: Given:x1,y1=-2,4, x2,y2= -1,-1m=y2-y1x2-x1

Q: If f(1) = 2 and f '(x) ≥ 3 for 1 ≤ x ≤ 5, how small can f(5) possibly be?

A: Given f1=2f'x≥3 ; 1≤x≤5

Q: Your firm has been asked to design a storage tank for liquid petroleum gas. The customer’s specifica...

A: Let r be the radius of the cylindrical tank andhemispherical ends, and let h be the height of thecyl...