21. 5₁ 1 dx (A) 2 So to dx dx both diverge when p = xP (B) 1 © DO dx and (E) -1 HOR LAY A DUPA

Q: Using trigonometric substitution to solve: sin 2x + C 8 cos x√3-cos²x sin 2x 4 cos x√4-sin²x secx 8…

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Q: dx 1-x² -2

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Q: The demand for a product is given by D(x) = 150e-0.025x, where x is the number of units sold each…

A: Let's find.

Q: Given: (1+2x) ex dx. Using integration by parts and letting u = -1-2x, dv = f(x)dx, then the value…

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Q: Given the function C(a) = (x-4) (x + 6) (x - 1) its C-intercept is its x-intercepts are

A: Solution is given below:

Q: Compute the quadratic form x Ax for A= Xx₁ 12 - a. x = b. x= 1 X2 a. x¹Ax= 3 2 [1] 10 C. X = and…

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Q: Find f'(1) given that f(x) ax+b cx+d' where a, b, c, d are constant.

A: we have to find derivative.

Q: Question 3 3x² + 5x + 2 Let f(x) 2x² + 71 4 This function has: 1) A y-intercept at the point 2)…

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Q: Determine the values of r for which the given differential equation has solutions of the form y =…

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Q: F(x) = integrate (3t + 2) dt from 2 to x + 2.  Use  first fundamental theorem of calculus to find…

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Q: Question 10 > Put a dot on the vertex of the parabola below. What is the coordinates of the vertex?…

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Q: Find f(x) if f'(x) = f(x) = 20x - 99 Of(x) = 20x² +1 O f(x) = 20x + 25 +5 Of(x) = 20x f(x) = 20x + C…

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Q: Given the function f(x) = -6 x -9 Evaluate f(8) = Find a when f(x) = 3 I

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Q: Find the total area bounded by the x-axis and the curve y = f(x) on the indicated interval. f(x) =…

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Q: d (h) (cot ¹(2)) = d (i)=(sec ¹(1))= = d (j) (csc-¹(2)) = dr 1 du 1+² dz 1 du I√²-1 dz 1 du I√²-1 dr

A: Given problem:-

Q: IV. Do as indicated. 1 1. Let f(x) Find the equation of the tangent line to the graph of f'(r) at…

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Q: Find F'(x). +2 x+² (4t + 1)dt a. F(x) = b. F(x) = ft³dt sinx c. F(x)=√t dt d. F(x) = f sin t² dt e.…

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Q: Given : A B Ⓒ E b 27π²-24 [x³sin(2x) dx = . 64 2π 3 3π 4 TU 4 =|m 5 T 6 Find b if Isb -SOST

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Q: Using trigonometric substitution, what is √x²-9dx ? f x3 A sec (-) √x²_9 6x² +C B ¹ (1) - V +C (ⒸC)…

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Q: if any. Find the absolute extremum point (s) of f(x) = el-cos on [-],

A: f(x)=e1-cos xf'(x)=e1-cos x ddx(1-cos x)f'(x)==e1-cos x (sin x)f'(x)=0e1-cos x (sin x)=0e1-cos x ≠0…

Q: Find the average value of the function over the given interval and all values of x in the interval…

A: Given query is to find the average value ifbthe function.

Q: Question 3 Given: (1 + 2x) e-x dx. Using integration by parts and letting u = -1- 2x, dv = f(x)dx,…

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Q: (D² – D − 2)y = cos x

A: Here is the solution:

Q: Write an equation for the quadratic graphed below: x-intercepts: (-1,0) and (4,0); y-intercept:…

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Q: -2/√√/3 dx x√√x²-1 • [²/²2 (x + 12/²3). dx sin² π/6 28. • √2 30.

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Q: The IBP formula fudv-uv- - fvdu can also be written as fudv + ſ vdu = uv Which of the following…

A: Given that the four options  To find choose the correct option which is satisfi IBP formula

Q: Question 14 If f(x)=x+4 and g(x) = -4, (a) f(g(x)) (b) g(f(x)) (c) Thus g(x) is called an function…

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Q: Question 12 5x + 5 Given: f(x) 4z-4 Find the inverse function, f-¹(z). =

A: Given query is to find the inverse function.

Q: Question 1 > Consider the parabola given by the equation: f(z)--22²-12z+7 Find the following for…

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Q: 23. ["Se' dx 5e* 2 24. S/2 ze de dx 2x

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Q: d Calculater₁(t) · r₂(t)] and [r₁(t) × r2(t)] first by differentiating dt the product directly and…

A: r1(t)=cos(t)i+sin(t)j+5tk,r2(t)=4i+tk,r1(t).r2(t)=(cos(t)i+sin(t)j+5tk)(4i+tk)r1(t).r2(t)=4cos(t)+5t…

Q: Identify the surface that corresponds to the equation 100y^2 - 25x^2- 4z^2 = 1. O elliptic…

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Q: Consider using the method of partial fractions to solve x²+x+1 Sa 2x²+2+x²+x A In(x²+1) B x+2 D…

A: This is a problem related to integration of the function using partial fraction decomposition. Based…

Q: Find T(t) and N(t) at the given point. x = T(0) N(0) = = = e cost, yet sint, z = e; t = 0

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Q: A bacteria population doubles every three hours. The initial population is 700. (a) Write a function…

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Q: -2√4x²+k

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Q: Find a set of parametric equations of the line through the point (1,-2, 3) and perpendicular to the…

A: Concept: As we know that a equation of the line through the point (α,β,γ) and perpendicular to the…

Q: sec+2x tan 2x and -dx 11 1 I + 12 tan 2x 16 tan³2x Ⓡ (cor³2x) ( 1+3csc22x 12 Ⓒ/cot²2xcot³21+C 16…

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Q: 12. lim [ln(t) sin(t)] t→0+

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Q: 7. Determine all relative extrema or saddle points: f(x, y) = 4x³ + 8xy - 2y²

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Q: f/²sin (co COS () sin (²) dx (Consider initially the first 2 terms) ATT/A a dr

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: The height y (in feet) of a ball thrown by a child is 1 y 162² +42 +5 where a is the horizontal…

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Q: Do as indicated. 1 1. Let f(x) = Find the equation of the tangent line to the graph of f'(r) at the…

A: Given  function f(x)=1x2+1 we want find the equation of tangent at the point where  x=1

Q: Question 1 sec42x Find -dx tanº2x -=(corº2x) ( 11 12 tan62x cot22x- - (cort2x) A - 1/1 (0 (A) B…

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Q: 1. S =dx = -Arcsin x√x²-4x-1 +2 X √5 +c

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Q: dp p(-75+25p²) 2 S. Trigonometric Substitution

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Q: Sketch a graph of f(x)=(x-2)² +4 6.

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Q: (3x-x²) dx x² Reciprocal Substitution

A: Let's find.

Q: Calculate the difference quotient for f(x) = x + x¹ at a = 9. (Express numbers in exact form. Use…

A: Here is the solution:

Q: 4x /² sin () cos (+) sin (²) dx (Consider initially the first 2 terms) 3

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