1. Evaluate the following limits. L'Hopital's rule is NOT allowed |2x - 1| tan-¹(¹) 2x - 1 . lim x-0-

Q: Your answer is incorrect. Evaluate the definite integral. NOTE: Enter the exact answer. Ld+23|| =…

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Q: Find the limit. lim → 2 (1 i=4j+ 1² k) i. lim 1-2(ti-4 j+¹² k) = + j+ k

A: evaluate the limit component wise

Q: Solve the given initial value problem. O x¹y² - xy³ = = 84 x³y² - y² = 26 x¹y² + xy³ = 78 x³y² + xy³…

A: Let's find.

Q: y"+9y=2e³x

A: Given; y''+9y=2e3x So, we can also write as; D2+9y=2e3x So, the auxiliary equation is; m2+9=0

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

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Q: Find a power serie CAPS |||| Determine the interval of convergence. (Enter your answer using…

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Q: Consider using the method of partial fractions to solve x²+x+1 rb Sa 2x²+2+x²+x - dx = [Af(x) – B…

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Q: Find E (p) for the price demand equation and interpret the results. x = f(p) = 1200(50p) where p-$28…

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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: 2. (D² + 3D + 2)y= 1+ 3x + x²

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Q: Find the solution of the given initial value problem in explicit form. 1 y' = (1 - 11x)y², y(0) - -…

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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: e²+2y + sech T = cot y + log2 (tanh x)

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

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

A: Let's find.

Q: Solve the differential equation and simplify (D^3 + D)^2y = 0

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Q: d Calculate dt [ri(t) · r₂(t)] and [ri(t) × r₂(t)] first by differentiating . dt the product…

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Q: The IBP formula fudv=uv-fvdu Which of the following statements fits and satisfies the equations? can…

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Q: Using mathematical induction. Prove that Ž {i= n(n+1) WHEN 12 1 2

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Q: a. Find the volume of the solid obtained by rotating the region bounded by y = x³, y = 8, and x = 0…

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

A: This question can be solved using the concept of dot and cross product of two vectors and…

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 10 Terry is skiing down a steep hill. Terry's elevation, E(t), in feet after t seconds is…

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Q: Using trigonometric substitution, what is sec-1 (-) √x²-9 6x² + C sec (1) √x²-9 6x² + C sec-¹ √x²-9…

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Q: 12 || ti + t²j||dt = |

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Q: The radius of a circle increases at a rate of 2 m/s. Find the rate at which the area of the circle…

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Q: √x²-9 √ di Using trigonometric substitution, what is f - dx ? x3

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Q: fe²x+Inx² sin x² dx = e2x cos x² dx

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Q: Evaluate the following limit using L'Hospital's rule. lim (e⁹x x⇒0+ 6x) ( ) +

A: Using LHospital Rule , limit is evaluated.

Q: π/4 x³ dx (x²+4)5/2 ST/4 (Use trigonometric substitution)

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Q: Question 7 Consider the Quadratic function f(x) = 9x² 4. Its vertex is ( Its largest z-intercept is…

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

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Q: If f cos42t dt = At - B sin 2t cos 2t + D sin 4t cos 4t + C where A, B, C and D are constants, 2A-3B…

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Q: dy II. Find Do not simplify your answers. da 1. log3 (√2x² + y) + tan(x - 7") = sin ¹1 (x²-1) +

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Q: π/4 x² dx (x²+4)5/2 ST/4 (Use trigonometric substitution)

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Q: x² dx (x²+4)5/2 Sπ/4. (Use trigonometric substitution)

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Q: graph each function using transformations or the method of key points. Be sure to label key points…

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Q: Question 4 Solve the equation: 1²+t+19-0. Fully simplify all answers, including non-real solutions

A: The given equation is: t2+t+19=0

Q: (x + 2)(6x - 1) (6 - x)(4x + 2) Find the horizontal asymptote of f(x) = 4- y=

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Q: Using trigonometric substitution to solve: f sin 2x +C 8 cos x√3-cos²x 1 + C 8 secx√4-sin²x sin 2x…

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Q: Integration of Algebraic Functions By trigonometric Substitution dx 6. S x²√4-x² dx 7. S- √81+x² X…

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Q: The general solution of y' = Y can be written in the form = C

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Q: IV. Do as indicated. Use Squeeze Theorem to evaluate lim sin(sinh x) csch z.

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Q: (A) = and B = . Find the vector projection of A D onto 2A - BO O O none of the above

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Q: Determine the interval(s) on which the vector-valued function is continuous. (Enter your answer…

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Q: A 0 B) 48 32 D) 96 If f cos42t dt = At - B sin 2t cos 2t + D sin 4t cos 4t + C where A, B, C and D…

A: The given problem is solved below in detail.

Q: V. Given: if x ≤ 2 el3r-6-2, [2x - 5], 13 f(x) if 2 3 √x²9, 1. Determine if f is continuous or…

A: Solution is given below:

Q: Question 13 Graph f(x)=x²-10x + 24 below by first selecting the correct shape, clicking the vertex,…

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

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Q: √ 1 x²√2x-x² dx = x+¹√ √√2x-x² + c 3x²

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Q: Evaluate the definite integral. NOTE: Enter the exact answer. S||ti + t²i||dt =

A: The given integral is converted to another form by using the following formula and then evaluate the…