(2) secxtanxdx e definite integral by substitution: -21 1- (2) dx (3) [x√x-2dx

Q: Find the solution of y" − 8y' + 16y = 0, y(0) = 1 and y'(0) = 5. y(t) = Ae4t + Be-4t y(t) = e4t+te4t…

A: The given equation is;  y''-8y'+16y=0, y(0)=1 and y'(0)=5.

Q: The sum of one number and five times the second number is 50. A. What are the numbers so that their…

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Q: 16. J x² 4 + x² dx

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Q: Given the following characteristics, select the function family that is described. Shape: single…

A: We need to select the curve which describe above charecteristics÷ Linear Linear graph has single…

Q: Given the partial decomposition of the rational function for some numbers A, B and C. What is the…

A: Given :x+1(x-1)(x-2)(x+3)=Ax-1+Bx-2+Cx+3

Q: area of a rectangle is fixed at 60 square meters. The base is increasing at a constant rate of 2…

A: Given the query is to rate of change of height.

Q: =1 Let R be the region bounded by the functions f(x) = -x² - 4x and g(x) = as shown in the diagram…

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Q: 21) Write a function that has an infinite discontinuity at x = 100. 22) Write a function that is…

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Q: Car X is travelling west at 20 kph and Car Y is travelling south at 30 kph. Both are headed for a…

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Q: D. Graph each of the given functions and solve for the area of the region that they enclose. 2. 4.9…

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Q: |x-3. Find flexo :)? f(x) = \ / . \

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Q: Verify that * / II 21 ?х ду 224 ду ох - for f(x, y) = 4x4y3 - 6xy5.

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Q: 2x² + x³ 3x² + 4x-9 1² +1 Q(x) + p(x) 1²+1

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Q: 10. Prove the identity: 2 + cot² (x) _ 1 = sin² x - csc² (x)

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Q: 11. A dangerous toxic pollutant has been accidentally spilled in a lake. t The speed of water…

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Q: Question R is the region bounded by the functions f(x) = 2e - 2 and g(x)=x²-5. Find the area of the…

A: We have to find out area

Q: -1.30 Find the value of the integral 100 √x dx by using simpson method (n = 6)?

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Q: Use Lagrange multipliers to find the critical points and the relative extrema. f(x,y,z) = x² + y² +…

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Q: 12

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Q: Find Vf at the given point. f(x,y,z) = x² + y² -32² + z lnx, (1,4,5) Vf|(1,4,5) = 7i+ (8)j + (-30)k…

A: Topic = Derivative

Q: 3) Evaluate for ln(x + 1)dx x

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Q: Evaluate x² √x² + 25 -2 S dx

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Q: A body cools from 75°C to 70°C in 2 minutes. What will additional time (in minutes) it takes to cool…

A: Topic:  Newton's Law of cooling using application of calculus

Q: Find Laplace Transform for 1-f(t) = 2t³; 2-f(t)=3e-²¹. 4-f(t)=2 cos(3t). 3– f(t)=sinh(2t); 5-cosh…

A: We have to solve given Questions.

Q: Equation Conversion from Rectangular to Polar Coordinates x=rcos 8 y = r sin 0 1. Convert each…

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Q: 0 ✓1+13xdx

A: Given that ∫021+13x3dxSolution:let 1+13x=t313dx=3t2dtdx=3t213dtat x=0,t=1at…

Q: 0 2 4 1 3 9 17 31 ? Question Plot the data from the table on the graph, where x represents the…

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Q: Find a Maclaurin series for f(x) = x2 e–x giving the first four nonzero terms and the general term.

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Q: Choose the correct answer for Wronskian, W for the following differential equation, y"-y=9e*…

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Q: b)show that: I(cosh at cos at) = 5²440*

A: This is a problem related to laplase transform. Here we will use convolution theorem for evaluating…

Q: In evaluating 5 3 Add your answer dx is same as evaluating lim (In(f(x))). Determine the value of…

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Q: 2. Find an equation for the plane that passes through the points P = (2,-1,3), Q = (0,0,5) and…

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Q: 10) x² + y² - 28x - 6y + 189 = 0 12) x² + y² - 32x+22y+376 = 0 2 14) x² + y² - 4x + 24y + 144 = 0…

A: Standard form of a circle is x-h2+y-k2 =r2,    where h, k  is the center of the circle and r is the…

Q: By using substitution of x-e' and t = ln(x), find the general solution of the differential equation.

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Q: What is y2 = 3x in polar form? r = 3 sin 0 sin 0 O Option 4 r = 3 csc 0 cote Option 2 r = 3 sin 0 -…

A: Given y2=3xTo find polar form:

Q: The graph of r = -2+3 cos is symmetric with respect to the O x-axis and origin origin only

A: given r=-2+3cos∅   it is the equation of limacon.

Q: In 1991, there were 41,144 shopping centers in a certain country. In 2001, there were 48,157. (a)…

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Q: Determine the graph of g = x^2 + sqrt of (x + 1) and solve for its extrema, concavity, and points of…

A: Please see the below picture for detailed solution.

Q: Let g(x)=6x-4. Find g (Type an integer or a fraction.)

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Q: Give the domain and range. Then, use the graph to find (a) f(-2). (b) f(0), (c) f Ay 40 & M 2 X and…

A: Answer: The solution is given below:

Q: L²x√x-2dx

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Q: 4x² + 4y² = 4y - 8x + 5?

A: equation can be written as 4x2+4y2-4y+8x-5=0 ⇒x2+y2-y+2x-54=0 Recall: if the general circle equation…

Q: Function: f(x) = 6 - 12x + 2x3 Find: Critical points, maximum, minimum

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Q: y= In x

A: Given function is y=x/ln(x)

Q: Determine the absolute extrema of the function ?(?) = sqrt of x - 9 on the interval [9,45]

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Q: When air expands adiabatically (without gaining or losing heat), its pressure P and volume V are…

A: We have to find the rate of change of volume.

Q: Solve the following deferential equations a) (x² - 4xy - 2y²)dx + (y² - 4xy - 2x²)dy = 0. e-2√x : 1…

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Q: Estimate the slope of the line given to the right. Select the correct choice below and, if…

A: slope of line = (y2 -y1)/(x2 -x1 ) here y2 = 5 y1 = 0         x2 = 1    x1 = 0 slope = (5-0)/(1-0)…

Q: [²³ 0 ✓1+13xdx

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Q: A lighthouse is on an island 350 meters east of the shore of Lake Bella. The lighthouse beam makes a…

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