Suppose that in a memory experiment the rate of memorizing is given by M'(t)= -0.009t² +0.8t where M'(t) is the memory rate, in words per minute. How many words are memorized in the first 30 min (from t=0 to t=30)? *** In the first 30 minutes words are memorized

Q: Decide whether the integral is improper. 1,01 In(x5) dx

A: We are asked to find whether integral is proper or improper

Q: Determine whether the improper integral diverges or converges. S™× x²e-x dx converges diverges…

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Q: The f sin 2x cos 2x dx is 1+3 cos 4x 1 sin²4x + C 24 1 In|1 + 3 cos 4x| + C 12 {A} {B} {C} - In|1 +…

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Q: - x³ + x² + 2x + 1 (x² + 1)(x² +2) da

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Q: Q/ By uesing chain rule Find du de For this functions E² +1 x² + y² X x = tanzt, y = e 2x a = / 11 ?

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Q: Find a Cartesian equation for the curve and identify it. ² cos(20) = 1

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Q: y = 1- cos 0 1+ cos 0 3

A: Solution of given question is written in below steps.

Q: Find the area of the triangle below. Carry your intermediate computations to at least four decimal…

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Q: owin - y" −4y' +4y=0 L".

A: 1)  y''-4y'+4y=0 Auxillary equation is m2-4m+4=0m2-2m-2m+4=0m(m-2)-2(m-2)=0(m-2)2=0 ⇒m=2,2

Q: The f2e4t sec2e4t dt is {A} = = tan e 4t + C {B} = sec³e4t + C 16 {C} /e4t tan e4t + C {D} et…

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Q: 1 - √xdx

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Q: Consider sin¹x cos³x dx. If we let u= sinx, the integrand can be transformed to

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Q: 32 Question * (3 Points) The proper transformation for sin²x to make the f sin²x dx readily…

A: substitution

Q: Determine whether the improper integral diverges or converges. 00 x²ex dx 0 O converges O diverges…

A: Given query is to find integral converges or diverges.

Q: Use the formula k(t) k(t) = ||r'(t) × r"(t)|| ||r' (t)||³ = r(t) = t²i+t³j to find k(t).

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Q: Given: y = cosh cosh (ex²)

A: Formulas:ddx cos hx =sin hxddx ex =exddx xn = n xn-1

Q: Find a, and d for each arithmetic series. 61. $20=1090, 420= 102 63. S16-160, a16-25

A: Given that : S 16 = -160 and a16 . = -25.  is for a arithmetic series.   And we find the value of a1…

Q: Evaluate the definite integral. J01(e 20t i+e-t j+t k)dt e 20-120 i-(e-1-1) j+12 k e 20-120-(e-1-1)…

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Q: 7.3 = x + 2y x-2y y'

A: This question can be solved using the concept of differentiation.

Q: The f e²x +e-2x e2x-e-2x dx is -2x1 {A}={In 2x te e e2x-e-2x + C 2x {B} In|e²x −e-²x | + C {C} -2…

A: To solve the given integral using substitution.

Q: Decide whether the integral is improper. [In(x³) dx proper O improper Explain your reasoning.…

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Q: . Given the fx²dx, which of the following is the integrand? C. x² A. 0 B. 2 D. dx

A: To determine what is integrand.

Q: The cos³4 dy is {A}-sin+sin³¹+C 3 4y 4 3 3 {B}sin-sin³¹+ C 3 4 3 (c)-sin-sin³+C {D}sin+sin³+ C

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Q: 13-16 Sketch the region whose signed area is represented by the definite integral, and evaluate the…

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Q: Find the laplace transform of f(t) = 21² +41 - 5 F (s) = F(s) = O O -5s² + 4s + 4 53 -555 +454 45³ -…

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Q: Find the curvature and the radius of curvature at the stated point. r(t) = = 11 cos(t)i + 9 sin(t)j…

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Q: 2. dx ***S 1 - x4

A: Integral

Q: 3.In 2 X 3x + 1) = ² ₁ X ‚ y'

A: Let us consider the expression, ax+by=c Using Implicit differentiation on both side we get,…

Q: 5. Use spherical coordinates to evaluate [[[ (x² + y² + 2²) ² dv D where D is the solid hemisphere…

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Q: Find J²w дх ду дz if w — ехух = 0.

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Q: Find T(t) and N(t) at the given point. T() = N K2 r(t) = 9 cos(t)i +9 sin(t)j + tk; t= 2 =

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Q: Convert the following lines to parametric equation. a) l₁: = (1,0,1) + t(1,0,−2), t = R Z-3 b) 1₂: x…

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Q: A. The series is absolutely convergent. C. The series converges, but is not absolutely convergent.…

A: From the given series we have to check the convergent and divergent of the series.

Q: As shown in the figure below, Mai is standing 100 feet from the base of a leaning tree. The tree is…

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Q: Find the Definite Integral Exactly and use Desmos to explain what you just found. -2 3. S²(x² - 3*)…

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Q: For the following: a) Determine the intersection points. b) Draw a sketch of the graph. c) Find the…

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Q: So whats the answer

A: The question asked for the function f or ft. The last line was the answer.

Q: 1. find dy/dx of each equation using implicit differentiation. a. x2 - y2 = 9 b. 3x2 - y3 -3xy = 0

A: As we know that; The Power law; ddxxn=nxn-1 The Product rule; f·g'=f'·g+f·g'   Given: (a). x2-y2=9

Q: Evaluate the following: 1) f sin x sin(cos x) dx

A: Integration

Q: 1. A man on a wharf, whose hand is 8.2 m above the level of the water surface is pulling a rope tied…

A: Given;  Rope length =20m Height =8.2m

Q: valuate the triple integral ***"* sin² (z)ze-²v³ dzdyda

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Q: f cos(mx) cos(nx) dx is equal to {A} [sin(m + n) + sin(m − n)] dx {B} [sin(m + n) - sin(m - n)] dx A…

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Q: Find the arc length L of the graph of r(t). r(t) t L= = ³²³i + 1 j + 1/2 √√61² k, 25157 = i

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Q: Determine the angle between the two lines: 1₁: 7 = (1,0) + t(0, —2), t ¤ R x+2 y-3 and 1₂: *+² = −³.…

A: Given

Q: Let m(x) be the slope of the tangent line to the curve y = 2x³-6x² + 3x at the point (x, y). Find…

A: Given: y=2x3-6x2+3x

Q: Find the laplace transform of f(t) = 6t³ + 4t² 3 F (s) = F (s) F (s) = F (s) = F (s) F(s) = -85³ +…

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Q: Evaluate the following 1. S sin x sin (cos x) dx

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Q: he equation of the line that passes through the point (-4,-2) and is parallel to the line y=4x-8 is…

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Q: Income flows continuously into a manufacturing company at the rate of 36, 450e 0.052t dollars per…

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Q: Activity 4: Determine whether the functions below are continuous or not on a given point or a given…

A: A function f(x) is continuous at a given point x=a   if following conditions are hold: (I)…