Find the general solution to: dy X xẩy = xảy x²y d y = o y = Cet² ° y = Cezx² ○ y = ex² ez x² + C eźx y = + C

Q: Q2: Solve the following integrals: (1) f 7x²+14x+15 (x²+3)(x+7) 02 dx ; u nein!! sin x+cos x (2) […

A: We have to calculate the given indefinite integral according to the given information

Q: C): Solve the following equations:- (1) sin 2x + 2 sin² = 1 (2) sech x - 4 tanh x = 1

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Q: Calculate the double integral. 16 9(1+x²) 1+ y² dA, R = {(x, y) | 0 ≤ x ≤ 5,0 ≤ y ≤ 1}

A: Please see the below picture for detailed solution.

Q: (d) Determine the y-intercept(s). (e) Sketch the function. (f) Determine the axis of symmetry. (g)…

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Q: Use L'Hopital's to determine the limit. lim 0 0 1 1-cos x I O sin x COS X as x approaches 0

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Q: ΒΣ 3 Θέλη

A: 3.The given series ∑n=0∞3.12n

Q: Find the area of the given region. y = sin(x) y 2 R|4 + + T Зл T

A: In this question we have to find the area of the given region.

Q: Find the average rate of change for the function over the given interval. y = ex between x = -2 and…

A: topic- average rate of change of function over interval Note: As per bartleby guidelines,we are…

Q: Approximate the definite integral using the Trapezoidal Rule and Simpson's Rule with n = 4. Compare…

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Q: Use the figure below to find the exact value of the trigonometric function of angle A. sin(A) 00 7 A

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Q: Solve the initial value problem y" — 2y' — 15y = 0, y(0) = a, y'(0) = −9. Find a so that the…

A: Given: y''-2y'-15y=0, y(0)=α, y'(0)=-9

Q: Use the comparison theorem to compare Enter your answer using either ≤ or >. F = = [₁* (√x + I + 2)…

A: We will use comparison theorem to compare the given two Integrals.

Q: determine if u and v are orthogonal, parallel or neither u=3i + 6j v=9i+12j

A: We need to determine if u and v are orthogonal, parallel or neither u=3i + 6j v=9i+12j

Q: Solve the given initial-value problem. y(x) = = y" + 6y'7y - 11e2x, y(0) = 1, y'(0) = 1 = -7.x 7e…

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Q: Find the Taylor or McLaurin series for the following functions X f(x) = 1 + x², a=0

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Q: [ 81e-9 sin 9xdx

A: Please see the below picture for detailed solution.

Q: Q3 :(A): By using "L' Hopital rules "; Find the limits of : (2) limx-o x-³ (tan-¹x - x)

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Q: dp dt Suppose that the current population is 100,000. (a) What is the predicted rate of growth 3…

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Q: .2 .4 S 7 iti ti ti ti 1+ -14 ។ 11 2

A: it is very basic question of complex number.

Q: (B): Find the tangent equation to the curve y = sin² x at point x = = 33.

A: The curve y=sin2x at point x=π3

Q: Use geometry (not Riemann sums) to evaluate the following definite integral. Sketch a graph of the…

A: This question can be solved using the concept of geometry to solve definite integrals.

Q: sint F(x) = √"* ( *ª*** ( √ ¹ + uª) du) dt Jo

A: The Fundamental Theorem of Calculus says: F(x)=∫ag(x)f(t) dt⇒F'(x)=f(g(x))g'(x)

Q: The function g is related to one of the parent functions  g(x) = |x − 1| + 5 a.) Identify the parent…

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Q: (B): Find the tangent equation to the curve y = sin² x at point x =

A: I have stated the used formulas in the solution.

Q: 3. Find the volume of the solid formed by y = √√4sin(x) bounded by x = 0 revolved about the x axis…

A: According to the question we need to find out the volume of revolution of the curve.

Q: (12) Find the derivative of the function Y = cos (a³ + x³)

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Q: If R is the region bounded by the graphs of the functions f(x) = 2 + 5 and g(x) = x + ½ interval [1,…

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Q: (B): Find the tangent equation to the curve y = sin²x at point x =

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Q: Use the figure below to find the exact value of the trigonometric run tan(A) 7 A

A: The solution is given below

Q: Given F(x) below, find F'(x). Provide your answer below: F(x) = I 4 (414 + sin* (t)) dt

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Q: Find dy ду é^sinx in sx

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Q: 1 2 Identify the true statements. Incorrect 3 4 56 f(1) is a local maximum. f(5) is a local maximum.…

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Q: Use substitution to evaluate the definite integral given below. 1² (Enter an exact answer.) Provide…

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Q: 2. Integrate the rational function below without using partial fraction decomposition. S -dv

A: Integrate the rational function below without using partial fraction decomposition v2/(v6-1)

Q: Evaluate INIM -6 x³ dx √x²-9

A: To find out the definite integral.

Q: 15. Show that the equation, 2³ + e* = 0 has exactly one real root.

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Q: given u = and v= find u*v

A: To find out the dot product u*v

Q: Q5: Find for the following functions: dx (1) In(x - y) = xy + y³; (2)y=tan³ √/cot(7x); cash? -nh.…

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Q: Q5: Find for the following functions: dy dx (4) y = x sinh 2x - cosh 2x

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Q: Find the tangent equation to the curve y = sin² x at point x = 3.

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Q: (B): If A = 2i + 3j-4k; B = 3i-4j+ 5k and C = i + j-k, find: (iv) (3A + 4B). C (1) A.B (U) B.C (iii)…

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Q: e −1 -1 lim (−1) t⇒0 t

A: Use limit expansion

Q: Q1/ Solve the following differential Equations. 1- (1+x2)dy-xy dx = 0

A: To solve the differential equation.

Q: what about part (b) please.

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Q: given the surface revolution x^2+z^2-5y=0 find the equation of its generating curve in the yz-plane…

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Q: Find the limit as x approaches 3 for x²-3x 2x²-5x-3

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Q: Suppose f(x)dx= 2 and f f(x) dx = 1, and f3f(x)dx=-6, what is B. 2 C. 3 D. 4 A.-2 f(x)dx?

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Q: Q2: Solve the following integrals: (1) 7x²+14x+15 (x²+3)(x+7) dx ; (2) sinx+cos x sin³ x cos³ x

A: Since multiple questions are asked, I am answering first question

Q: 2. Approximate 64.1 by using linearization and use a calculator to compute the percentage error.

A: Given :64.13

Q: Suppose that a particle moves along a straight line with velocity v(t) = 10 - 1t, where 0 ≤ t ≤ 5.5…

A: Given: v(t)=10 -t, 0≤t≤5.5