Let us recall the following Antiderivati a. f sinx dx = -cos x + C b. f cos x dx = sin x + C C. f sec² x dx = tan x + C

Q: Find g'(x) for each of the following functions. 4) g(x) = sin(u²)du 5) g(x)=₁*Inu du

A: Solution: The objective is to find the derivatives of given functions

Q: Given the graph of f(x) below. Determine the average rate of change of f(x) from x = -5 to x = -3.…

A: We need to find average rate of change.

Q: Solve the given differential equation. All solutions should be found. dy x³-8y dx x NOTE: Use c for…

A: The given first-order differential equation is: dydx=x3-8yx⇒dydx=x2-8xy⇒dydx+8xy=x2...(1)

Q: 10) y7 exbx

A:

Q: Find the area of the region above the curve y = x^2 - 6, below y = x, and above y = − x.

A: Given region bounded above by  y=x2-6  and y=-x  and bounded below by y=x

Q: 4 Find the general Solution of the following PDES • з Их + 2 Иу -Х ucx, c) - че 2 (зу-2х)12 ans3-…

A: To find the general solution of the given PDE .

Q: 9. Find the volume of the solid obtained by rotating the region R enclosed by y = -x² + 6x-8 and y =…

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Q: cos(bx) sin(bx) dx

A: topic- indefinite integral

Q: VSDE of tan xdx + y * cos^2 ((x) * dy) = 0

A: (Sinx/cosx)dx+ycos²xdy=0 (Sinx/cosx)dx=-ycos²xdy (Sinx/cos³x)dx=-ydy tanx sec²xdx+ydy=0 Integrate…

Q: Ixe xex/3 dx

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Q: I. Simplify. Write "undefined" for expressions that are undefined. -1 5 -3 6 3 3.) 5 0

A: We have to find out product

Q: 2 убличк In'/xl alx

A:

Q: Function h is graphed. ← -4 -3 -2 -1 Find ["h(2) dz. [²h(z) dz = [ Y 4 3- 2+ 1 -1 -2- -3- -4 h 1 2 3…

A: The given graph is:

Q: Determine the roots of y"" - 4y" + 3y = 0

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Q: Let f : R 7−→ R be defined by f(x) = 2 − 5x. Show that f is bijective, and find f^(−1)(x).

A: Let f:R→R be defined by f(x) = 2 - 5x.

Q: Given that f(z) = z-z where does f'(z) exist

A: Concept: z  is represented as  z=x+iy And its complement z¯ z¯=x-iy For f'(z) to exits only if…

Q: Find the volume of the solid obtained by rotating about the x-axis the region bounded by the curve y…

A: The volume (V) of a solid generated by rotating the region bounded by y=f(x) and the x‐axis on the…

Q: 4. Evaluate the double integral: L Later y¹/3 x² +1 (Hint: Change the order of integration to dy…

A: Given: I=∫08∫y132yx7+1dxdy The region bounded by the curves x=y13, x=2 from y=0 to 8.

Q: Does the following series converge or diverge? 4√n Σ 3/2 10n +7n+7 n=1 O The series diverges. The…

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Q: dy Write down a differential equation of the form dx 17 all other solutions diverge from y = as t →…

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Q: II. Find the inverse of each matrix. 5 -11 -9 1. -7 DO 8

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Q: Find the solution of the given initial value problem. y = ²7y= y' cos t t-7 Y(T) = 0, t> 0 y(t) =

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Q: 2. Express the iterated integral as a double integral in polar coordinates. 1 X 1 Lo dy dx 16/2 x² +…

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Q: 13 By direct partial integration, Solve the following PDES s. 8²u ахбу = CEX COSysXu(X,t) Ex UCH, y)…

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Q: 3) Use L'Hopital's Rule to evaluate and check your answers numerically: (a) lim x→0+ (sina) 1 (b)…

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Q: 6 By separation of variables, Solve the following 5 PDES :- учи ²4 dx2 0 o u(e,t) = u(5,t) =6 u(x,0)…

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Q: Find Domain and Range бяц tue Ⓒsin (x+3) +2y x²+2y 3x + y² 3) 3x + Sin (3x) +2y+Z² Ⓒ x+2y cos2x…

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Q: y ye 2x+4 tax

A:

Q: I. 4. Evaluate each determinant. 2 -5 2 -1 4

A: We have to find out determinant

Q: (1) Let I be a proper ideal of the commutative ring R with identity. Then I is a ........ if and…

A: Given : Let I be a proper ideal of the commutative ring R with identity. Then I is a _______ if and…

Q: find the solution of following differential equation using Laplace transformation. y" + 3y + 2y = ex…

A: Let's solve given diffrential equation by using laplace transform.

Q: 31² If the velocity function of a moving particle is given by v(t) = 6 – + x, find the position…

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Q: Let F(x,y)=ln(x² + y2), then answer the following (1) Find the function's domain (2) Find the…

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Q: The output of an economic system Q, subject to two inputs, such as labor L and capital K, is often…

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Q: 2-S Sin ³ x cos" x dx

A: SOLUTION-

Q: 4. Evaluate the double integral: To fo (Hint: Change the order of integration to dy dr.) y dx dy.…

A: We have given the double integral in which the region of integration 'R' is given below  R : { 0 ≤ y…

Q: find the derivitive, r'(t), of the vector function.  r(t)=a+3tb+t^7c

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Q: Differentiate the function. f(x) = x²(x + 8) f'(x) = x³ (x + 8) 3 X

A: In this question, we need to find the derivative of the given function.

Q: Evaluate sin (x) e-x dx by use Simpson's rule. h=0.5

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Q: a. The volume of R using cylindrical coordinates with dV = r dz dr de where R: 0 ≤ x ≤ 2,0 ≤ y ≤ √4…

A: Let's set up  triple integral in cylindrical coordinates.

Q: Problem Revolve about the (a) x-axis and (b) y-axis the area enclosed by y²=x and y=x³.

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: When applying the convolution theorem to calculate: a 8 L-1 ¹ { x² + Q² * x² +F}" You obtain the…

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Q: 1. Let R be the region in the first quadrant enclosed between the circles x² + y² = 9 and x² + y² =…

A: x= rxos(theta) y= rsin(theta)

Q: - x, then answer the following (1) Find the function's domain (2) Find the function's range. (3)…

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Q: Given a second order differential equation dx 2x = e³t dt where t = 0, x = -5. Using Laplace…

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Q: Given the function f(x,y)=e5-2x+3y, approximate f(4.1,0.9)using point (4,1) for (xo, yo). What is…

A: The linear approximation of f(x, y) at (a, b) is the linear function  L(x, y)=f(a, b)+fx(a,…

Q: S- tanh e cosh(z) – sinh(z) -dz

A: Let's evaluate given integral.

Q: Write out the first four terms of the Maclaurin series of f(x) if f(0) = -9, f'(0) = -9, f(x) = +...…

A: Topic = Series

Q: 12. A thin 4 cm wire represented by 1 < x < 5 has density function p(x)=19/cm. Find the mass of the…

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Q: 3(a) The cost of manufacturing motor cycles (per day) is related to number to number of motor cycles…

A: Here we have to use the concept of derivatives.