d 1 (a) / (₁2²+ = + 2²/² +6² +5) X dx d ex (b) (x³ sin(z) +2+1) dx d (ln(tan-¹(x))) dx (c)

Q: 2x+3 (2x² + 6x - 1)5 S 1)5 dx

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Q: Solve the given initial-value problem. y(x) = 7e y" + 6y' - 7y= 11e2x, y(0) = 1, y'(0) = 1 2x -7.x +…

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Q: Q5: Find for the following functions: dy dx (1) In(x - y) = xy + y² ;

A: Find the derivative

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

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: Solve the initial value problem y" + 4y + 4y = 0, y(-1) = 5, y'(−1) = 6. y(t) = =

A: The given initial value problem is y''+4y'+4y=0,  y(-1)=5, y'(-1)=6

Q: Given f" (x) = 8x − 6, ƒ' (1) = −3, and f(1) = 5 find f(x).

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Q: Use the figure below to find the exact value of the trigonometric function of angle A. sin (A) 6 A…

A: it is very basic question of trigonometry.

Q: S 2 (2 x ² + 1 ) 1²/1 2 dx

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Q: 1-). 25 2-) 3+4i 3-1

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Q: Use polar coordinates to find the limit. [Hint: Let x = r cos(8) and y = r sin(8), and note that (x,…

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Q: 9. f dx 3x²√√25-x² 10. √ √² + 2tdt 11. f 3x+1 -dx 3x³-2x²-4 12. x²(x-1)(x+2) dx

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Q: Find the lengths of the missing sides if side a is opposite angle A, side b is opposite angle B, and…

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Q: The graph of y = f(x) is shown. Use the graph to answer the question. Is f continuous at x = -4?…

A: The graph of the function y = f(x). With the help of this graph, we have to show that, Is the…

Q: 19. For a given function, f(x) = ³ - 15x² + 48x + 2, (a) Find the interval(s) on which f is…

A: Note to student :    Thanks for posting your queries. But there are  multiple parts given. As per…

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: Evaluate the following limit. t sinj+ sin = 1+ k t -k π lim costi-5 1-x

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Q: cos¹3 xdx 2. Dễ sin12xcos®xdx 1.

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Q: Compute u v if u and v are unit vectors and the angle between them is R|4

A: we know that u.v =uvcosθfor unit vector u=v=1given θ=π4

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: Evaluate the indefinite integral f7 sin v cos vdv =

A: Given ∫7sin6v cosv dvTo evaluate the integral:

Q: Use the given conditions to write an equation for the line in point-slope form and slope-intercept…

A: We have to find out find slope form

Q: For the vectors u = (6, 3, 4√5) and v= (3, 0, 5√5), evaluate the following expressions. a. 3u + 2v…

A: See this solution in below

Q: 7. Use the Method of Lagrange Multipliers to find the extrema value of a function f(x, y, z) = 2x² +…

A: Concept: Lagrange multipliers: A straightforward and elegant technique for determining the local…

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: x-1/2c (4) y = x sinh 2x – cosh 2x

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Q: Prove that (3-2)(x+2) = 3+2i ifitues.

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Q: Simplify the following with out 1) -5, 3+1 using the denominator

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Q: Find the indefinite integral using any method. (Use C for the constant of integration.) (sin(0) +…

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Q: Sketch the space curve. Function r(t) = (5 sin t, 3t, 5 cos t) 1.0 0.5 0.0 0.0 -0.5 -1.0 -5 N 0.5…

A: Please see the below picture for detailed solution.

Q: Use the limit definition of partial derivatives to find fx(x, y) and fy(x, y). f(x, y) = x2 − 4xy +…

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Q: In Exercises 37-42, use the Shell Method to find the volume obtained by rotating region A in Figure…

A: See this solution in below

Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) x + y lim (x,y) → (0, 0) x²…

A: To evaluate: lim(x,y)→(0,0)x+yx5+y

Q: Evaluate the function at the given values of the independent variables. Simplify the results. f(x,…

A: topic- Functions

Q: Find all the values of x such that the given series would converge. (x-8)" 8n n=1 The series is…

A: We will use ratio test.

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: 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: Approximate the area of the region bounded by the graph of f(t) = cos (t/2/2) and the t-axis on…

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Q: (B): Find the tangent equation to the curve y = sin² x at point x = T-3 π .

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Q: Solve the initial value problem 25y" — 40y' + 16y = 0, y(0) = 2, y'(0) = 3. y(t): How does the…

A: We can solve this as follows:

Q: Find a power series representation for the function. f(x) = X 8 - x³

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Q: Find the general isolation of the following: 1. (x³y³+1)dx +x4y²dy=0

A: Please see the below picture for detailed solution.

Q: The graph of y = f(x) is shown. Use the graph to answer the question. Find lim x-(-1)- O-2, -7 O-7,…

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Q: A particle moves along a line with a velocity v(t) = -2t+4, measured in meters per second. Find the…

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Q: Find the limit. lim (x,y) → (5, 1) ety Discuss the continuity of the function. O continuous…

A: See this solution in below

Q: 3. The radius of a sphere ball is measured at r = 25 cm. Estimate error in the volume and surface…

A: The radius of a sphere is measured at r = 25 cm. We have to estimate error in the volume and surface…

Q: Q5: Find dx for the following functions: (1) xcinh 2x coch 2x (3) y = e* sin² x In√x

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Q: If f′(−6)=7, and g(x)=−3f(x), what is g′(−6)? Do not include "g′(−6)=" in your answer. For example,…

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Q: FIND: hf(x)dx 2 g(x) dx = = f₁₁ f(x) dx = = if g(x) is an odd function. if f(x) is an odd function.

A: We need to find integral.

Q: Solve for the value of constant(C) by obtaining the orthogonal trajectory of the given equation…

A: I have stated the used formulas in the solution

Q: 3 2.)f x³ (4 + x²)² dx ; Use rationalizing substitution

A: