Book Problems 51 - 53 Use series to evaluate the following limits. Give only two non-zero terms in the power series expansions. 1+5x-e5z x2 +.... lim #40 1+5x-e5x x²

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A: **As per our guidelines, we are supposed to answer only one question with a maximum of three…

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A: Concept used

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Q: Let f (x) y=x+4 y=x y=x+2 y=x-2 x²-x+4 x-3 . what is the equation of the oblique asymptote of f(x)?

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Q: for part b for the partial derivatives, how did you get 6K–1/2 L1/4 – 1.2 and 3K1/2 L–3/4 – 0.6,…

A: The solution is shown below-

Q: Evaluate the following line integral along the curve C. Six-y (x-y)ds; C is the line segment r(t) =…

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Q: Find all of the solutions of the equation on the interval [0, 2n]: tan²xsinx = sinx. O 0, п, 2n

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Q: 3. What is the degree of h'(x) for the function h(x) = (x + 3)¹(x − 2) 5? 8

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Q: Problem 16. Find all CP of f(x) = arcsin x-2x. Note that

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Q: Consider F and C below. F(x, y, z) = yzex² i + eײj + xye×z k, C: r(t) = (t² + 5)i + (t². (a) Find a…

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Q: Use a suitable half-angle formula to find the exact value of sin(15°)

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Q: Question 3. Find F where and F(√) = 3. F'(x) = 2x cos(x²)+7√√π

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Q: SD-SF in 1 hour 7T Without using a calculator, what is the value of the following function? cos 12…

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Q: calculate the volume of the shape obtained by rotating the region bound by f(x)=e^(-x^2,) x=1, and…

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Q: Use the Law of Sines to solve the following triangle for c. Approximate your answers to the nearest…

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Q: Use suitable sum-to-product formulas to rewrite the following expression in terms of tan3x. sin 2x +…

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Q: Is the function f(x) = 2√x - 3+4 continuous over his domain?

A: We have to check whether the function  is continious over his domain.

Q: If y = and w=, then the projection of v onto w is: 0 O O

A: We have,      v =<-5, 2>      w=<-1,-2>

Q: Determine which set of vectors has an angle of 90° between them. Ov=(-10,5), w = (1,-2) Ov=(3,1), w…

A: To find out the set of vectors having 90 degree angle.

Q: Find the critical points/numbers as well as the extrema of the given function.( 3 f(x) = 3x² + 4x³ -…

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Q: A plane travels N45°E at an airspeed of 1000 km/h. Measurement on the ground shows that the plane is…

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Q: nd the distance between the skew lines: c = 8+9t, y = 2 +9t, z = 4-6t x = 8-t, y = 7, z = 2 + 5t…

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Q: Use Heron's Area Formula to find the area of the triangle. (Round your answer to two decimal…

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Q: For the given functions f and g, complete parts (a)-(h). For parts (a)-(d), also find the domain.…

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Q: 1. Find the derivative. Simplify as needed. (a) f(x) = sin(x) (b) g(x) = sin (e) (c) h (t) = et…

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Q: 1- Compute dy/dx, tan x a) y = xt

A: Note:Since you have posted multiple questions we will solve the first question for you. If you want…

Q: Use derivatives to determine where f(x) = 2x^3 - 9x^2 + 12x - 3 (a) where the function is increasing…

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Q: The result of a dot product is a scalar. True O False

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Q: 3. Graph the inequality: y2(x-1)2. Label the vertex. Test one set of coordinates that satisfies and…

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Q: Find a vector a with representation given by the directed line segme A(0, 4, 4), B(4, 4, -2) Draw AB…

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Q: Find the minimum cost of a rectangular box of volume 160 cm whose top and bottom cost 6 cents per…

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Q: 3) Find y' if y= e ²x

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Q: y=7+ 2x +9xex; a=0 The equation for the tangent line is y= Use a graphing utility to graph the curve…

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Q: Find the derivative of the given functions using the Differentiation Rules. 2. g(x) = x3-5x²+6x+1…

A: Rule of derivatives

Q: Find the size of the obtuse angle (to the nearest degree) between the two curves y = ln (x² +1) and…

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Q: Determine the derivative for y ду = ?х ду ?х ду ?х ду ?х 5 cos (2x-4) = = 5 sin (2x - 4) = 10 cos…

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Q: 17. r(t) (te, 2 arctan 1, 2e¹), 1-0

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Q: Cosines - Summer 20 x O Law of Sines O Law of Cosines…

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Q: 10. Determine dy of y = 5-2x+7 dx In 5 -2(5-²x+7) ○ (5-2x+7) In 2 ○ (5-²*+7) In 5 ○ 2(5-2x+7) In 2

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Q: A triangular plot of land has sides of lengths 320 feet, 250 feet, and 80 feet. Approximate the…

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Q: The population of Mathvill is modelled by P (t) = (0.37)-² +3, where the population is measured in…

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Q: 14. a. As x→→∞, f(x) → c. As x→-3˚, f(x) → e. The graph is increasing over the interval(s) g. The…

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Q: The information in the following problem allows you to construct 1 triangle. A = 30°, a = 1 m, b = 2…

A: A=30° a=1m and b=2m