The following can be derived from the above rules. log,1 = log, a = log, d' = loga log 1 b= log, blog, c = log d" =

Q: For the region bounded by y = 2x, the x-axis, and x = 4, determine which of the following is…

A: We have to find whether the volume about x-axis and y-axis are equal or not.Fo that we will…

Q: (3x-y + 1) dx- (9x-3y-3) dy = 0

A: Given differential equation:- (3x-y+1)dx-(9x-3y-3)dy=0

Q: Find the volume of the solid obtained by rotating the region bounded by y = -x^2 + 6x - 8 and y = 0…

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Q: how long will it take for the population to reach 140 grams

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Q: Solve: 52+31 x-5 ≥ 1 HE (Enter your answer in INTERVAL notation, using U to indicate a union of…

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Q: 14 cout 5. + 3+ 2 2 -2+ -3- ress play to show imation Watch the values of f(x) as the x value…

A: To determine what y‐value is fx getting closer to as x approaches 1 from the right side.

Q: 6. For f(x)= x², write the linear approximation at a = 1 and estimate f(1.05).

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Q: A function f(x) is continuous at an x value of aif and only if the following three conditions are…

A: Concept If a function is continuous at x = a then limx→a-f( x ) = limx→af( x ) = limx→a+f( x )

Q: cos²x-1 COS X = - tan x sin x

A: We have given equation to prove cos2x-1cosx=-tanx sinx Taking left side of the equation  LHS…

Q: Let f(x) = 2x² + 9x +9 3x² + 20x + 25 This function has: 1) A y intercept at the point 2) x…

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Q: x²sin+y²cos + xy In X X X+Y x-y

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Q: Determine the following: a. S 1 √2x²+8x+9 dx

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Q: Solve the Initial Value Problem. π y' = tan (y), y(In (7)) = (Express numbers in exact form. Use…

A: We have given differential equation  y'=tany dydx=tany 1tany dy=dx     Integrating both sides…

Q: The line tangent to the graph of y=x3 at the point where x=0.2 crosses the x-axis at the point…

A: We have given equation of the curve  y=x3 Put x=0.2 y=0.23 y=0.008 Say,  x1,y1=0.2,0.008…

Q: (x² + y²) exp(2x) + 4) 4xy

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Q: 9-h² 2. lim h 3 h 3

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Q: For the given acceleration vector a(t) = 6ti+ (2t+ 1)j−12k and initial velocity vector v(0) = −4i +…

A: Given acceleration vector a( t ) = 6ti + ( 2t + 1 )j - 12k  initial velocity vector v(0) = −4i + 2k…

Q: In Exercises 7-16, evaluate the limit. X x → ∞ x + 9 7. lim 8. lim x →∞ 3x² + 20x x →∞ 2x² + 3x³ -…

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Q: The graph is the following function. f(x) = x sin ( 10 ) {x # 0} and 0 {x=0} The function is…

A: If a function is continuous at x = k then limx→k-f( x ) = limx→kf( x ) = limx→k+f( x )

Q: n x + 3xn-kyk +yn 2 x² - y²

A: Given: fx,y=xn+3xn-kyk+ynx2-y2 To find: whether the function is homogeneous or not, if yes find the…

Q: Find the inverse Laplace transform L-¹{F(s)} of the given function. 12s² - 21s +54 s(s² +9) Your…

A: Given function:- Fs=12s2-21s+54ss2+9

Q: M(x,y) dx + (y³ + x2y + x) dy = 0

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Q: H. JJ HY BY 4.6 where y(0)=0 y'co)=2

A: Given differential equation is y''+4y'+3y=4e-x with y(0)=0 and y'(0)=2We know the formula that PI of…

Q: Compute the derivative of the vector-valued function. r(t) = teti + tln(t)j + sin(6t)k (e¹(t+1),1…

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Q: A dinghy is pulled toward a dock by a rope from the bow through a ring on the dock 10 ft above the…

A: We know that Pythagoras theorem " In a right-angled triangle, the square of the hypotenuse side is…

Q: By determining f'(x) = lim h→0 f(x) = 6x² = f(x+h)-f(x) h (Simplify your answer.) find f'(4) for the…

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Q: Find the limit. (If an answer does not exist, enter DNE.) x² - 6x + 8 X-4 lim X→ 4

A: To evaluate the following limit. limx→4 x2-6x+8x-4

Q: 4 3 T -2 -1 √ 3- 2- 1 0 -1- -2- -3- -4. 7 2 3 O 4 Continuous ? Are any of the statement true? Use…

A: To find whether given function is continuous at x=3 or not.

Q: 4. Find an equation of the tangent line at the given point. at (2,√5) a. y² = = x-1 x²+1

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Q: Find the volume of the solid generated by revolving the region enclosed by x=√10y², x = 0, y = -1,…

A: Let's find volume of the solid.

Q: Find a formula for f-¹(x) if f(x) = 1, ≥ 0. 5 x²+1,x

A: To find a formula for f-1x if fx=5x2+1, x≥0.

Q: Given the Lorenz curve L = x2.59 find the gini index.

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Q: Find the inverse function of y = g(x) = 5x³ + 5 g¹(y) = √25(x-5) 5

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Q: Evaluate the indefinite integral. | a2ea3 dx + C

A: To evaluate the following indefinite integral. ∫x2ex3 dx

Q: Find the horizontal and vertical asymptotes of the curve. 9ex ex - 8 y =

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Q: Solve by completing the square x2−6x−4=0.  The solution set is {____} (Simplify your answer. Type…

A: To solve the following quadratic equation by the method of completing the square. x2-6x-4=0

Q: 1 7. For f(x) write the linear approximation at a = 0 and estimate f(-0.1). (Note: The derivative of…

A: Let's find value of f(-0.1).

Q: 4. lim_ x² (1 - e¹/²) using l'hopital

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Q: (4) Given & & unit vectors and 1²₁³)=³/2 Find 12-31

A: Given  e and f are unit vectors.

Q: Determine an equation for the plane passing through the point P(-4, 2, 0) and containing the line…

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Q: Evaluate the indefinite integral. 4x + 2 -dz x² +1 [1

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Q: Find the volume of the solld generated by revolving the following region about the given axis. The…

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Q: each limit. You may use the provider

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as a…

Q: An object is thrown upward at a speed of 128 feet per second by a machine from a height of 11 feet…

A: given  h(t)=-16t2+128t+111) put  h(t)=168

Q: Integrating an odd function (without considering the arbitrary constant of integration) will give…

A: Let f(x) is an odd function then,                             f(-x)=-f(x)                ⇒…

Q: For the graph f(x) above, find: Find: lim f(x) = x→6- lim_f(x) = x→6+ lim f(x) = x→6

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Q: In a binomial distribution, the value for 'q' is 0.14. Therefore, the value for 'p' is: 0.14 0.86…

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Q: Two events are non-mutually exclusive. If P(A) = 0.51 and P(B) = 0.34, what is the probability of…

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Q: (siny-2ye¯*sinx) dx + (cosy + 2e-*cosx) dy = = 0

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Q: Find the values of where the tangent line to the graph of f(x) Give exact answers (not decimal…

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