(d) Determine the y-intercept(s). (e) Sketch the function. (f) Determine the axis of symmetry. (g) Determine the minimum or maximum value of the function. (h) Write the domain and range in interval notation. Write your answers in exact form.

Q: A. Find the following limits. Answer four only. x-¹-1 i. ii. iii. lim- X-1 X-1 lim 4x-x² X-4 2-√√x…

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Q: Evaluate the indefinite integral f7 sin v cos vdv =

A: Given ∫7sin6v cosv dvTo evaluate the integral:

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Q: cos¹3 xdx 2. Dễ sin12xcos®xdx 1.

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Q: Evaluate the following limit. sin xy + cos xy 2y lim (x,y) →(0,)

A: The objective is to evaluate the limit.

Q: Sketch the function. v(x) = 0.2(x-3)²(x+2)³

A: We can answer the question as below.

Q: · 1. -1 (3-2x) ³ dx

A: The objective is to evaluate the integration.

Q: 3 2.)f x³ (4 + x²)² dx ; Use rationalizing substitution

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Q: (C): Solve the following equations:- (1) sin 2x + 2 sin² = 1

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Q: Describe the domain and range of the function. F(x, y) = 5x² - y Domain: 0 {(x, y); x = 0} 0 ○ {(x,…

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Q: Q2: Solve the following integrals: (1) f 7x²+14x+15 (x²+3)(x+7) 02 dx ; u nein!! sin x+cos x (2) […

A: We have to calculate the given indefinite integral according to the given information

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Q: 1. Given the space curve r(t) = (2e¹,e²¹.e^¹), find the curvature at t = 0

A: I am attaching image so that you understand each and every step.

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Q: Find the shortest distance between the point A (3, 10) and the line y = x + 1.

A: Our Aim is to find the shortest distance between the point A(3,10) and the line y=12x+1 -(i)

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

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Q: If R is the region bounded by the graphs of the functions f(x) = 2 + 5 and g(x) = x + ½ interval [1,…

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Q: For f(x)= x+1 and g(x)= find X a. (fog)(x); b. the domain of fog a. (fog)(x) = (Simplify your…

A: The given functions fx=xx+1 and gx=11x

Q: Find a differential equation whose general solution is 8t y = c₁est + c₂e-2t. = 0

A: We can find the differential equation as below.

Q: Skill Building In Problems 13-24, use the graph on the right of the function f. 13. Is fincreasing…

A: Please see the answers below.

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A: Given: y''-2y'-15y=0, y(0)=α, y'(0)=-9

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Q: -9 (x-1) 8. √x dx

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Q: dy 5: Find for the following functions: dx (1) In (x - y) = xy + y³; (2) y = tan³ √/cot(7x); (4) y =…

A: Since we are given with multiple number of question and answered according to the guideline

Q: 818 B. Find the horizontal, vertical, and oblique asymptotes of the curve y =

A: In this question, we want to find the vertical, horizontal and oblique asymptote of the given curve.…

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A: Please see the below picture for detailed solution.

Q: Find the indicated limit by using the limits 6f(x, y) lim (x,y) → (a, b) g(x, y) lim (x,y) → (a, b)…

A: Given: lim(x,y)→(a,b)f(x,y)=3lim(x,y)→(a,b)g(x,y)=-5To find:lim(x,y)→(a,b)6f(x,y)g(x,y)

Q: In 100 yrs, 132mg of radium decomposes to 96mg. How many mg will be left after 200 yrs?

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Q: Q5: Find dx (1) In(x - y) = xy + y² : (4) y = x sinh 2x-cosh 2x for the following functions: (2) y =…

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Q: • Solve for the value of constant(C) by obtaining the orthogonal trajectory of the given equation…

A: The objective of the question is determine the orthogonal curve for the given curve.

Q: Use the substitution u= x² + 6 to find the following indefinite integral. Check your answer by…

A: To evaluate the integral.

Q: 04: Answer two only: (A): IF A-2 10 1-2 -1 Find AB and AC. 3 and C-0

A: Given :A=420210-2-11B=2312-2-2-121C=31-3026-121

Q: 2x+3 (2x² + 6x − 1) b. f 1)s dx

A: B only Integrals by Substitutions

Q: (B): If A = 2i +3j - 4k; B = 3i - 4j+5k and C = i + j - k, find: (iii)A. (B+C)and (A + B).C (iv)…

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Q: Q3 :(A): By using " L' Hopital rules "; Find the limits of: 1 2 (1) limx-o[: 1-cos x sin²x (2)…

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Q: 04: Answer two only: (A): I A-2 1 -1 1-2 Find AB and AC.. -- 3 1 1 and 1 3 1 CO

A: Given :A=420210-2-11, B2312-2-2-121, C=31-3026-121

Q: Find dy x 3 In (x - y) = xy + y²

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Q: Q1: Fill in the blanks for the following statements (chose five only) 4n 1. lim-00 2n+1 2. log10 (3x…

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Q: (C): It w = tan x and x = 4t³¹ +t: Find d?

A: Given that w=tanx  and x=4t3+t. We have to find dwdt. We can write,  dwdt= dwdxdxdt  [ using chain…

Q: In Problems 17-26, solve the initial value problem. dy y(0) = √3 dx y' = x³ (1-y), 1 dy 2 dx dy…

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Q: Use partial fractions to find the power series of the function: n=0 4x + 41 (x − 2)(x + 5)

A: To find power series for the given function.

Q: Let r(t) = (e²t, e−³,5t) Calculate the velocity vector and the acceleration vector at t = 0.

A: r(t) = ( e2t , e-3t , 5t ) given  find velocity vector and acceleration vector    velocity vector…

Q: 2. y(x4-y²)dx + x(x++y²)dy = 0

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Q: For what values of a and b is the line 2x + y = b tangent to the curve y = ax² when x = 4?

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Q: dy Q5: Find for the following functions: dx (3) y = et sin²x In√x

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Q: Solve the following differential equations: (1+x²) (dy-dx)=2xy dx

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