Matching Type. Match the functions in Column A with their corresponding antiderivatives in Column B. Column A Column B S 1.dx , a. tan-1(*)+C 9. Sz 2.dx b. sin-'(*)+ C 5 idx 3.' xvx2-1dx C. sec-1x + C 4.' V25-x²dx d. tan-1x +C 5. 81+x?dx e.sin-'x +C

Q: Determine the absolute maximum and minimum values of the function f(x) =+x the interval -2sxs2. x…

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Q: Evaluate the indefinite integral, ſx² sinh x³ dx.

A: To evaluate: I=∫x2sinh x3dx⇒I=∫sinh x3  x2dx

Q: Find the inverse transform, indicating the method used and showing the details: 2s - 10 -5s 1. s3 3s…

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Q: 27. f(1) = 1 + e*" 28. f(1) = r² - eW + 5 29. f(1) = (1 + e?)2 30. f(1) = (e' – e")? 31. f(1) = 412…

A: Given÷

Q: SIn(5 + Vr)dr Algebraic Substitution

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Q: 5. A Ferris wheel has a radius of 20m and takes 2.5 minutes to rotate once. a) How far does a rider…

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Q: Each side of an equilateral triangle measures 3cm, with a possible error of 0.1cm. Using…

A: The area of a quadrilateral triangle is: A=34x2 where x=side length =3 cm So, A=34(3)2=934cm2

Q: 5. S , dz dy dx 2 c3

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Q: 4. A car costs Php 800,000. Find its value after 4 years if it depreciates 20% of its cost per year.

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Q: 2. y=x² - 4x and y=-x² +2x. y² = x and x² –2x+3y= 2. 3.

A: Given÷

Q: Q2: Evaluate o o" y*(x² + y²)dx dy 1 cV1-y? y² (x? + y?)dx dy

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Q: dz az and ду Suppose z is a function of x and y, and tan Vy? + x2 = ze6y. Solve for

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Q: Determine the first derivative for each of the following functions. Remember to "Tidy" up your final…

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Q: -Sune +1

A: This question is based on solution of Trigonometric equation.

Q: Solve the initial value problem for r as a vector function of t. dr Differential equation: = - 22k…

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Q: cal | a*(a³ + 3)/4 dx. (+3)/4 dx. 4

A: integration

Q: Show that - 8. ==1+* +4++++1=

A: We know ∑1n2=π26  Hence, ∑1(2n)2+∑1(2n+1)2=π26 Therefore, 14∑1n2+∑1(2n+1)2=π26 ∑1(2n+1)2=π26 - π224…

Q: Find Valke of nhegal Sxdx X dx

A: To evaluate the given integral

Q: Find the volume generated by revolvingg the area bounded by the given curve and awd lines y = x', x…

A: Volume generated by revolving the area bounded by curve  y=x3  and line x=0  and y=8 (that is 8=x3…

Q: Let F(x) = (f(x))² + (f'(x))², F(0) = 6, where f(x) is a thrice differentiable function such that…

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Q: a?z B. For each of the following functions z, find a2z and ду? a²z дх? дудх' дхду" 1. z = 2x2 – 5xy…

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Q: 4. Evaluate the integral 2+ In? x -dx. x – x ln x (a) 3 ln |In a – 1| + 2(ln r – 1) + (In a – 1)2 +…

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Q: B. For each of the following functions z, find az az a2z and дх? дудх" дхду ay2 1. z = 2x? – 5xy +…

A: We know that when we differentiate a function partially with respect to 'x' , other variables of…

Q: 3. Php 120,000 is deposited in a savings bank that earns 9% simple interest per year. What will be…

A: given principal amount (P)=php 120,000 interest R=9% T=5years sum of amount after five year? formula…

Q: Calculus How many numbers are relatively prime to the following number. - 209 - 323 - 867 - 31…

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Q: Question 1 Compute v31.6 approximately by use of differentials. O 1.995 O (E) None of the choices O…

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Q: For numbers 9-11: Given a circle passing through the point (5,9) with radius equal to 4. 9. Where is…

A: Explanation of the answer is as follows

Q: cost- sint sint+ cos t i+ - cost- sint cost- sint i+ Find the binormal vector B and torsion t for…

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Q: '9 — х? dx x2

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Q: 3. Find the parametric equation of the line passing through the point (-1,0,3) and in the direction…

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Q: 1 3 5 8 - 37 13) 3 8. 7 Ans. r = 3 0 - 37 0 37

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Q: e problems y' + e = 0, y(0) = 1 %3D

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Q: 2eln In cos 2t 8 + 2 None of the choices Option 2 2s s2 – 2 s2 – 2 Option 5 Option 3

A: This question is based on Laplace transform.

Q: a²z For each of the following functions z, find a²z a²z and ду? дх2 дудх' дхду 2. z= sin3x cos4y

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Q: 2. Suppose z is a function of a and y and tan(V+ y) = e*. Determine dz dz and 2

A: Suppose z is a function of x and y  tan (√(x + y)) = ez^2  We have determine ∂z/∂x and ∂z/∂y

Q: 1. Evaluate the given line integral, (-y,x – y) · dR, where C is the upper part of x² + y? = 4 from…

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Q: Change the following rectangular equations to polar form. Show work on separate pape 14. x² +y =10…

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Q: Consider the curves x = 12y? and x + 6y = 18. a) Determine their points of intersection (x1, Y1) and…

A: Given :   x=12y2 x+6y=18

Q: Find aly if and of to

A: Differentiation

Q: give me an example of properties of definite integral

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Q: NONHOMOGENEOUS EQUATIONS: UNDETERMINED COEFFICIENTS  2. (D^2+D-2)y=2x-40cos2x Please answer this…

A: Here, the given DE is: (D2+D-2)y=2x-40cos 2x Now, to find the yh. The auxiliary equation of the…

Q: Use Method of Variation of Parameters: [D² - 8D + 16]y = e4Xsec2x

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Q: The approximation of / (x-3)e* dx by composite Trapezoidal rule with n 4 is: 4.7846 -25.8387 This…

A: Given:∫02(x-3)ex2dx

Q: 2. Consider the function g defined by 1 g(r, y) = cos (TI/y) + log3 (x – y)* Do as indicated. (a)…

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Q: x dx V3-2x-x

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Q: Find the volume OF the solid obtained by rotating about the y- axis the region bounded by Y= x2 and…

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Q: Зx+1 5. f(x) %3D 3x2+2

A: f(x)=3x+13x2+2Differentiate…

Q: 1 dx, if possible. State whether the integral converges or diverges. 4

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Q: Show necessary computation x²-9y? lim (x,y)→(1,0) tan-1 (x4 – 4xy + y²) lim (х,у)-(0,0) х-Зу b. а.…

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Q: e ( +5t –2) 6. 5 (s – 2) (s - 2)² O Option 3 O None of the Choices 6 + 5(s – 2)² – 2(s - 2)° (s -…

A: To find the Laplace transform of f(t)=e2tt3+5t-2⇒f(t)=e2tt3+5e2tt-2e2t