Find the indefinite integral and check the result by differentiation. COS X 1 - cos²x dx

Q: ess the function G in the form fog. (Enter your answers as a comma-separated list. Use non-identity…

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Q: Write an equation of the form y = mx + b for the line in the following graph. [Hint: Either find the…

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Q: If what does the following integral equal? - 11 [¯¯1² [8f(x) + 2g(x) — h(x)]dæ = - 68 - 11 [= f(x)…

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Q: Find the area under the curve y 7 x over the interval [1, 5]

A: Given curve y=7x

Q: What is the integrating factor of the differential equation (5xy + 4y² + 1) dx + (x² + 2xy) dy = 0?…

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Q: Consider the graph of f. f(z)dz (2) The shaded region over [0, 7] has an area of 314 and evaluate…

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Q: Convert the following equation to Cartesian coordinates. Describe the resulting curve. r= - 4 cos…

A: We  have given polar equation  r=-4cosθ-6sinθ Using cartesian equations x=rcosθ y=rsinθ x2+y2=r2 Put…

Q: if / 2³3 rsin rda -x³ cos x + 3x² sin x + 6x cos x Oxsin x O cos x sin x X COS X = 6 ƒ ƒ(x)dx, then…

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Q: it a rock is dropped from a height of 288 ft, its poistion t seconds after it is dropped until it…

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Q: The graph of g' is given below: W Notice this is the graph of the derivative of g not the graph of g…

A: Given graph of g' is shown below

Q: the interval that f(c) = k. there exists a value c, where <C Must there exist a value of c in the…

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Q: Use differentials and the graph off to approximate the following. (Round your answers to three…

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Q: Differentiate the following. Do Not Simplify. y=(sinx)(lnx)_ b) y=(e³+√cos x) c) y = º /1—tanx 3x³…

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Q: y=x5, mn=-1/80

A: Given problem:- Find the equation of the line normal to a given curve y=x5 and having a given slope…

Q: 52. y' - y = y³

A: We need to solve D.E.

Q: Find the solution to satisfying _y(t) = dy dt = 2y y(6) = 9

A: The given differential equation is; dydt=2y As we know from the integral rule,  ∫1ax+bdx=1alnax+b+C

Q: 04115

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Q: Given the curve shown below, determine if the slope of the curve at x = negative, or zero. 4 3 2 O…

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Q: intervals

A: A function is increasing if when y is increasing with respect to x ot vice versa. Hence, Given…

Q: Find the equation of the tangent line to y=−6/x^2 at x=−2. Write your answer in slope-intercept…

A: The equation of the curve is y = -6x2 To evaluate: The equation of the tangent line to the given…

Q: -6-5-4-3-2-1 у 7г 6 4 3 2 1- -1 -2 -3 -4 -5 -6F 1 2 3 4 5 6

A: Range :- all the y value where function is defined

Q: + 22/12 =)₁ y x² + y² dx + (ye³ +2²4₁²) dy = 0 =)

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Q: Which of the following is the solution to the differential equation dy = y³ce² that satisfies the…

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Q: On the Fahrenheit temperature scale, water freezes at 32º and boils at 212º. On the Celsius…

A: Degree and Fahrenheit

Q: Sam makes $25.00 per hour. He gets paid time and a half for overtime. He gets paid every week. He…

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Q: [2re™² dr a. 2xe*² + C b. x20x³ 3 @. ex² + C d. x²e² + C + C

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Q: State the domain: -6 -4 -2 6 2- 0 -2 2 4 6

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Q: 1. Carbon 14 is a common form of carbon which decays over time. The initial amount of carbon 14…

A: Please see the below pictures for detailed solution.

Q: lim 2-0 |3x-1| + 3x + 1| I

A: Given problem :- limx→03x-1+3x+1x

Q: Find the solution to the differential equation that passes through the origin. z(t) = dz dt = 6te42

A: dzdt=6te4z⇒e-4zdz=6tdtIntegrating both sides we get,⇒zt=-ln-12t2-c14

Q: Is the following piecewise function continuous? if x < 0 0<if x < 3 if 3 < x f(x) = -3x² x - 3, . -x…

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Q: Find la da without using the Fundamental Theorem of Calculus.

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Q: 3 3 3 2 (49) (+91 i- -74+ i n n n integral, that is provide a, b and f(x) in the expression f(x)dx.…

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Q: Calculate: fx²e³dx

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Q: y(x tan x + In y) dx + tan x dy = 0.

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Q: Evaluate the piecewise function at the given valuesof the independent variable. f(x) = { 5x+3 if x<…

A: Given piecewise function is  f(x) = { 5x+3 if x&lt; 0            { 4x+7 if x ≥ 0 We have to find…

Q: dv/du = (uv)² — 2(u — v) — 2.

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Q: Determine whether the function is differentiable, continuous, both, or neither at the value where…

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Q: -10 -5 f(x) 10 10 5 10

A: Note: Since the student has posted 2 sub-parts of the question in which the part (1) is complete and…

Q: Solve (x² 1 + 2y) dx + (1 - x²) dy = 0; when x = 2, y = 1 1) (x + 1 + 2 ln x 1|) b. (x + 1) y = (x −…

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Q: Solve the differential equation (2x + y) dx (4x + 2y − 1) dy = 0 O a. 5x 10y + In 10x 5y 2|= C O b.…

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Q: Solve the differential equation [cos (2y) — 3x²y²] dx + [cos (2y) - 2x sin (2y) - 2x³y] dy - a. sin…

A: Given: cos2y-3x2y2dx+cos2y-2xsin2y-2x3ydy=0

Q: y² = -25x 10- + the equation of the me focus is (Type an ordered pair. Type an integer or a…

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Q: A piece of cardboard measuring 10 inches by 8 inches is formed into an open-top box by cutting…

A: Given, Card board size  10inches ×8 inches By cutting squares with side x on each corner.

Q: Evaluate the following integral using integration by parts. Sxe ³x d dx Use the integration by parts…

A: We have given to find integral  ∫xe3x dx Let,  I=∫x e3x dx Using integration by parts ∫u dv=uv-∫v du…

Q: Question 13 (1 point) ✓ Saved Which of the following CANNOT be an acceptable direction vector for…

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Q: A particle moves along the x-axis so that its position at time 0 ≤ t ≤ 18 is given by x(t), whose…

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Q: Find the slope of the tangent line to the curve 2x² 4xy + 4y³ = 10 at the point ( − 1, 1).

A: SOLUTION-

Q: 3. State the components of a unit vector that is perpendicular to the vector =(5,2,-1).

A: To state the components of a unit vector that is perpendicular to the below vector v. v=5, 2, −1

Q: Solve the following initial value problem for the unknown function y(x) a) y' = 2xy², y(1) == b) 2…

A: Topic:- application of integration