Evaluate: cos32xdx cos³2x - +C 6. cos2x (A) cos32x +C cos2x B sin2x sin32x +C 6. = 2 sin32x + C 6. sin2x D = - 2

Q: 1. Find the following derivatives: d E In (1 + In(t)) dt A P B = In (1 + In(t)) dt dr 1/a d E| In (1…

A: Given problem:-

Q: Use Mean-Value theorem to find c X +2x-1 ; [o,i] xj[3,5] Use L'Hôspital vule to find the wmit lime…

A: We will solve the Problem on limits and mean value theorem.

Q: 3. Evaluate the following integrals: cos e G = de J (1 + sin 8) vsin 0

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Q: ax+3, if x <2 f(x)= It is given that f(1)=5 bx2 +2, if x 22 and f(2)=6. Find the value of f(a+b). О…

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Q: f(x) = x* - 2x? ... Choose the correct graph below. O A. В. C. D. Ay 10- -40

A: Given query is to find the graph is the function.

Q: Find the Taylor series generated by (a) f (x) = 2x at x =1 ( b ) f (x) = 2x3 + x2 +3x-8 at x =1

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Q: A. S', f(x)dx = B. If the vertical red shaded area in the graph has area A, estimate: a f(x)dx = -3…

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Q: Find the area of the parallelogram with vertices ?(−1,2,4), ?(0,4,8), C(1,1,5), and D(2,3,9).

A: Let us take  A = (−1,2,4), B = (0,4,8), and C(1,1,5).

Q: 5) = -?². (*+). Suppose that cos (x) = and cos (x + Find the value of sin (x + Make use of the…

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Q: sing reciprocal substitution *= the integral - dx reduces t I dz -1) 13 -dz (z?– 1) 1/3 zp- D dz

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Q: 1.) Evaluate: S(2+ y²)²dy 2.) Evaluate: S 1+sinx xp-

A: To evaluate the indefinite integrals:

Q: 1. Use the trapezoid (a) (b) (c) x In x dx; with (h = 0.1)

A: f(x)=x ln(x)   x 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 f(x) 0 0.10484 0.218785 0.341073…

Q: a. A*(CB) = (AC)*B %3D

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Q: amplitude: period: phase shift: 6.

A: Follow the procedure given below.

Q: sec? ede 2. tan' 0+9 tan e

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Q: Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval.…

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Q: Direction: Find the derivative of each of the following functions. Write your solutions on a…

A: We have to find the derivative

Q: 8 Convert the polar equation r 2 = -2 sin 2θ to a Cartesian equation. x2 + y2 = 2 xy ( x2 + y2) 2…

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Q: Find the distance from the point (5, -4, 1) to the plane −3x−2y−3z=−4

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Q: 2cos'z = COS T Select all correct solutions.

A: Follow the procedure given below.

Q: Which of the following is equal to sec 2 x tan³x dx to obtain the correct indef inite integral?

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Q: For the function f, use composition of functions to show that f 1 is as given. 7x -7 f(x) = 7x+1,…

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Q: Solve for the general and particular solution using Laplace Transform y" + y = v2 (cosvEt) %3D y(0)…

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Q: If $21.000 is invested in a savings account offering 4.5% per vear, compounded semiannually, how…

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Q: Find the horizontal and vertical components of the vector with the given length and direction, and…

A: For a vector v with magnitude M in the direction of θ.The Horizontal comonent is given by…

Q: Consider the alternating series (-1)"bn with n=0 1 bn = 1+ 8n4 Is the sequence {bn} increasing or…

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Q: sin5xdx – / sinxdx 2 sin2x cos3x dx=. A) True False B

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Q: Suppose g is a function which has continuous derivatives, and that g(8) =-2, g(8) = 3. g"(8) =-4,…

A: Taylor polynomial:g(x)=∑n=0∞ gn(a)n!(x-a)n  a=8g(x)=g(8)0!(x-8)0+g'(8)1!(x-8)1…

Q: Question 9 To evaluate J y-cse(y?)cor²(y³)dy, we let u =cse(y³) A) True B) False

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Q: What would be the shape of the graph r = 2 cos 0, given that 0 = 0, 7 , 5, 5? O semi-circle in the…

A: We know cosθ takes positive values in first quadrant that is for 0&lt;=θ&lt;=π/2 The equation…

Q: Numerically integrate f (x) = x³ + 3x? + 4x = 2 using Single-Trapezoidal Rule. 6 from a = 1 and b -…

A: (1) solution

Q: dx

A: We will use substitute method to solve this integrate

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Q: Find the slope of the line 3x-4y-10=0 О а. 4/3 O b. 3/4 О с. 3 O d. 4

A: Solve the following

Q: Use the graphing utility to plot the graph of y = tan on the interval [1, 50]. y = 2-8 y 2:45 2-1…

A: Let's find.

Q: Evaluate the line integral, where C is the given curve.   z2 dx + x2 dy + y2 dz,   C C is the line…

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Q: 1. Find the angle between the following two vectors. and

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Q: Select the answer option that corresponds with polar coordinates (4,-120\degree). 90° 2 W/2 150° 45…

A: Option

Q: Find a function y = A sin (B(x – C)) with the period a, phase shift 2, and amplitude 7. There is…

A: The general equation of sinusoidal function is: y=AsinBx-c Where,  A= Amplitude T=2πB=period c =…

Q: For the function f(x) = x ln(1+ x°), %3D a) What is the Maclaurin series for f and its interval of…

A: Given function is fx=xln1+x3Maclaurin Series of function fx…

Q: sin2x cos3x dx= sin5xdx – sinxdx A True B) False

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Q: The form of decomposing a single irreducible quadratic factor in agiven inteeral is / (2ax+b)A+B dx.…

A: To write that it is true or false.

Q: Σ (-1)"+1 n³+1 n=0

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Q: 2m '+e-2m ) dm=2 12m dm (А) True B False

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Q: x +1 8. J x(x+ 4)3 dx

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Q: . Using the vectors in the previous item, which of the following vectors makes an angle of 90° with…

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Q: Determine the intervals on which the following function is concave up or concave down. Identify any…

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Q: Problem 3. The softplus function is given by A2) = log(1 + e) A) Plot ſ(2) as a function of z. If…

A: (1) solution

Q: Use long division to divide. (x³+ 4x²+x+ 4)÷ (x+ 4) x²+ 8x+ 33 x2+ 1 120 x²+ 8x+ 33+ x+ 4 x²– 4 129…

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