Question 19 If f'(x) = cot² x + 1 and f(1) = 1, then ANSWER: Blank 1 Blank 1 Add your answer 1 f(0) Question 20 11

Q: Which of the following pair of points has slope m = -2? □ a. (-1,3) and (-5,-11) O b. None among the…

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Q: Given tan theta = 1  evaluate (without using a calculator): cot (90º - theta)  and  sec theta

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Q: Let f(x) = 7x√√/1-x², with domain x € [-1, 1]. Find the area of the region between the curve y =…

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Q: The velocity vector, v(t) of a particle in motion is given by v(t)=t√t² +4i+e²j+ -k. 2t+1 Find: (i)…

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Q: lim h-+0 (sin h)/h- cos h h²

A: Evaluate the limit using Maclaurin series limh→0sinh/h-coshh2=?

Q: 165. Use Green's theorem to evaluate S (y² + x³) dx + x^dy, where C+ is the perimeter of square [0,…

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Q: a. Determine whether the Mean Value Theorem applies to the function f(x) = * on the given interval…

A: a) f(x)=ex Interval : [0,9] We know that, f(x)=ex is continuous for all real numbers (-∞,∞) and it…

Q: нас 2 obtain the Fis for f(x)= X-X² in the interval [-^, ^] ? Solution ht! 2 ans : = = =+ 25 (1452…

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Q: 7P (2/27 +27) 9. 'TE

A: ∫tndt=tn+1n+1+cI=∫04(t2+t32)dt=∫04t2dt+∫04t32dt

Q: Find the values of x, y and z that correspond to the critical point of the function: f(x, y) = 5x² +…

A: Given that function is f(x,y)=5x2+4x-8y+3y2 Partial derivatives Partial derivatives with respect to…

Q: (1) =( 9-1², 7²²_,,sin (√1² −9)) Find the domain of the vector function, r(t) = {

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Q: Find the value of y for the given differential equation if the value of the arbitrary constants is…

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Q: The value of China's exports of automobiles and parts (in billions of dollars) is approximately f(x)…

A: Given query is to find the year when export will be 9.7 billion.

Q: Question -1 Given y' = x³y-¹ and y (4) = 3, what is y? Select the correct answer below: Oy=±√√√ 21…

A: Topic = Differential equation

Q: Evaluate the definite integral. 6.³ 0 2 1 + 1x² -dx

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Q: 6) The number of downloads of a certain app is 13.6 million in 2019, and 11.4 million in 2022.…

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Q: Write the standard equation of each hyperbola and the equations of the asymptotes: i) Center at the…

A: As per the requirement of the student part iv has been solved.

Q: Given that the position vector, r(t)=√√3 cos (21)i+2 sin (21) j+cos (21)k. Find (a) (b) the tangent…

A: We have to find the tangent, normal and binormal vector.

Q: F(x) = [ 2 1 | t dt

A: topic - integration and derivative we are given F(x)=∫2x1tdtwe know that∫1xdx=ln|x| +Cddxln(x)=1x

Q: Alejandra is attempting to drag her 34.6-kg Golden Retriever across the wooden floor by applying a…

A: Apply Newton's Second Law horizontally and vertically.

Q: The final should be 4 no? Not 23/6?

A: Given Vector:- F→x,y,z=lnx+y+xzπ,1+yzsinhy,zey-cosz

Q: Find the GS of y" + y = COS X sin x

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Q: Write the system in vector matrix form: b) x2 O d) C X' X² 3 0 -3 -2 2-2 1 2 1 -4 3 04 -1-3 2 2-22 3…

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Q: a. Determine whether the Mean Value Theorem applies to the function f(x) = -1 + x² on the interval…

A: We have given function  fx=-1+x2 (a) (i) function is continuous on the interval -2,1 (ii) function…

Q: x² 2 - 4 - lim x +∞ x O a. O b. +∞o O c. 0 - - O d. 4 -∞ O e. 1 O f. 2 O g. -4 Oh. -2 2 = O i. None…

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Q: PROFIT A manufacturer determines that when hundred units of a particular commodity are produced, the…

A: The profit function is given by: px=400015-xx-2 dollarswhere x is hundread units.

Q: Evaluate: 1₂ ნენ 76 + 3 dx 11

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Q: Find a function f(x) such that ƒ'(x) f(x) = – 6x² – 1 and ƒ(0) = 5

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Q: Centerville is the headquarters of Greedy Cablevision Inc. The cable company is about to expand…

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Q: f convergence of the power series n=1 n²

A: Given :

Q: Find the slope of the tangent line to the given polar curve at the point specified by the value of…

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Q: Find the are length of the parametric equations x=217/2 0st≤1. z=t;

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Q: If f(1) = −13 and f′(x) ≥ 31 for x ∈ [1, 11], how small can f(11) be?

A: Given query is to find the smallest possible value of f(11).

Q: Let f(t) be the weight (in grams) of a solid sitting in a beaker of water. Suppose that the solid…

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Q: 1. Let C be the parametric curve defined by dy d²y a. Find and dx dx² [x = tan-¹t Y | = | ln(1 + 1²)…

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Q: Question Find the general solution to the following differential equation: Use "C" for the constant…

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Q: If f is continuous on the interval [a,b], then which of the following four statements are always…

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Q: lim, 0 sinx − x 3

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Q: 3) Solve 24x-8 = 16 without using a calculator. 3 4) Separate log₂ (√x²√) into a sum of logarithms.

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Q: Sketch an excellent graph for the following equatic a) r = 2 cos(0) + 1 3π/4 TT/2 21 31 π/4

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Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (If the…

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Q: Determine the intervals on which the following function is concave up or concave down. Identify any…

A: Given that function f(x) = x4-2x3+6 First derivative f'(x) =ddx( x4-2x3+6)=ddx( x4)-2ddx( x3)+ddx(…

Q: Determine the location and value of the absolute extreme values off on the given interval, if they…

A: we know that absolute maximum and minimum occur either at end point or at critical point so first…

Q: Evaluate the following definite integrals using substitution. fx (1-6x²) dx 0

A: Given query is to find the value of integral.

Q: Find the sum of the series. 8 n = 0 (-1)^²n 62n (2n)!

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Q: If sin e = √√7 and cos Ꮎ = 4 what is tan Ꮎ? +1w

A: Given query is to find the value of tanθ.

Q: The acceleration of an object (in m/s²) is given by the function a(t) = 6 sin(t). The initial…

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Q: Find / (1,•r.) if r₁ = (1 + √1,e²³ ) a dt and r₂ = (7, In (2t)).

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Q: A house was valued at $100,000 in the year 1988. The value appreciated to $165,000 by the year 2004.…

A: A house was valued at   $100,000 in the year 1988. The value appreciated to $165,000 by the year…

Q: i. Evaluate the following integrals 2. S (²/²² - 12/17 - 1²/1) dx a. 3 √x x3

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