√=x if x<0 if 0≤x≤1 2x-x² if x>1 Let f(x)=₂x

Q: xsin (y) + ycos(x) = 1

A: To find the derivatives of the given functions.

Q: Solve: x^2dy - y(x+y)dx = 0 O x+y=Ce^(-y) y Ixl=Cx^2 x=Ce^(-x/y) O x lxl = Cy^2 Oy=Ce^(-xy) O y…

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Q: (a) The graph of y = g(x) is shown. Draw the graph of y=-g(x+1). 6 ?

A: We are authorized to solve only one question, please repost remaining questions Graphical…

Q: d- d³y dx3 d²y +69² y dx² - dy 15- dx 100y = 0 equation

A: Topic = Differential equation

Q: If y = (1+x)8 (x + 1)7 True False then dy dr

A: We can solve this as follows:

Q: The domain of the logarithmic function y = log4 (x + 3) is Ox>0, XER Ox-3, x=R Oxz-3,TER OX>0, XER

A: Let's find domain of given logarithmic function.

Q: Jo (sec 9x + csc 9x)³ dx

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Q: I Find the most general antiderivative of the function. (Check your answer by differentiation. Use C…

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Q: d- d³y dx3 ax d² y dx² +6- 15 dy dx Q.2-Solve the differential equation 100y = 0

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Q: 9. [ 2x + y cos (xy)] dx + x cos (xy) dy = 0

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Q: Indeterminate Form 4 7. lim 2 1–cosx x-0 4 1 8. lim x-2x²-4 x-2 9. limsin 3xcot 2x 10. limx²e 11.…

A: We have to determine the indeterminate forms.

Q: Carlos surveyed 50 students about their favourite subjects in school. He recorded his results.…

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Q: For the regions A and B shown in the graph: Part A: Discuss the limits of integration. Part B: Set…

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Q: 4. find the derivative 4v².4+ [7v¹.5-3v-2 Enter your answer

A: Given  Let y= (4v^2).4+(7v)^1.5 - 3v -2 y= 16v^2 + (7v)^1.5 -3v -2 Formula: (d(x^n)/dx) = n(x^(n-1))…

Q: 2. The subspace in R3 is a plane whose equation is x+y+z=0 x-2=0 x-2y+z=0 (a) (b) 2-0 (c) y-2--0…

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Q: Find the minimum value of the following function: f(x,y,z) = x² + 2y² + z² - 2xy - 2y + 5  using…

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Q: If we try to apply Rolle's Thorem to the function f(x) = 2x² – 20x – 5 on the interval [0, 14],…

A: Here, the given function is: f(x)=2x2-20x-5 and the interval given is [0,14].

Q: Q5: Find the inverse Laplace transform of: f(s) = 3²(²-3)

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Q: 02:- b. find the total differential dz. z = x sin xy + x³

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Q: Graph the parabola. y = (x+5)²+1 Plot five points on the parabola: the vertex, two points to the…

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Q: A tank initially contains 50 gal. of fresh water. Brine (water in which a certain number of pounds…

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Q: 5. If the variance equal 16, the standard deviation equal: OA. 4 OB. 10 O C. 5 OD. 3 O E.2 6. If the…

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Q: Find the solution of the given ODE. * x² + 3y² y 2xy Y = 1 Option 1 1 8 85 x = Cx = Cx 2 1 + ( ² ) ²…

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Q: Ismael made an error when he was evaluating log3 27 - log3 9. Ismael's work log3 27 - log3 9 log, 27…

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Q: x. e²ydy + (*²*¹) dx = ( 0 (Variable separable)

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Q: 2 61-19]. and C 3 3 Given the matrices A = В: 9 3 5 the matrix X in the equation (A - 5B) X = C. X =…

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Q: calculate the purchasing power of this amount

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Q: Evaluate the integral.   The integral from 1 to 4 of e^(4/x)/x^2dx

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Q: A consultant determines that the percentage of people who will have responded to an advertisement…

A: keeping a note ?as per our company guidelines we are supposed to answer ?️only first 3 sub-parts.…

Q: d dx sin(t) dt

A: We have to find derivative

Q: Solve the given differential equation by separation of variables. dy dx e³x + 4y =

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Q: c) f(x)=tan(cos².x) 11 COS X 1+ sin.x Dy=- b) y = 2

A: e)  f(x)=tan(cos2x)  f) y=cosx/(1+sinx) g) y=ex^2/x3 Repost the next part.

Q: 20- 18 16- 14- 12 10 Co 8 6 4 2 1 Estimate the instantaneous rate of change at x = 1

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Q: Find the partial derivative of z with respect to x дz (2x−y) дх Н дz 2 О 0 = 3 - 1 " дх Т 2y 2y дz…

A: Just use the rule of partial derivative and find the required solution.Final solution is in the box.

Q: Q:4) Use Green theorem and evaluate the line integral ${Mdx + Ndy} Where M(x,y)=y², N(x,y)=x², C is…

A: See the details solution in below

Q: Given z = 7t - 43 and y = 49 sin t dy (i) de to (ii) (1₂)

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Q: b. Determine the gradient of the following function at Po h(x, y, z) = cos xy + e + In zx, Po(1, 0,…

A: We need to find gradient.

Q: Evaluate the integral. (Use C for the constant of integration.) The integral of sqrt((4+x)/(4-x))dx

A: To evaluate the integration.

Q: 2|6x + 4 ≥ 1 OX- 7/12 O-7/12 - 12/7 choose the right ans оо

A: solution:-26x+4≥16x+4≥12using properties of modulus6x+4≥12  or  -6x+4≥12 6x≥12-4  or  -6x≥12+46x≥-72…

Q: x f(x) f'(x) x g(x) g'(x) 1 3 4 1 2 6 2 5 2 8 7 3 7 7 3 9 2 4 -1 4 5 -3 Using the tables, evaluate…

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Q: Find the Taylor polynomials of orders n = 0, 1, 2, 3, and 4 about x = x and then find the nth Taylor…

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Q: Transform each graph as specified below. (a) The graph of y=f(x) is shown. Draw the graph of y=f 5…

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Q: Given the matrices A: = [1-4] 0 21. B=( )-C-1) ₁ [1 -5 5 and C= the matrix X in the equation AX + 5B…

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Q: Obtain the orthogonal trajectories of y=Cx^2 and compute for the positive value of y of the…

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Q: Find f'(a) using the definition of the derivative at a point for: f(x). 1 = √x at a = 4.

A: Find derivative using  definition of f(x)=1x at a=4

Q: Problem 6. Find the equation of the tangent line to the curve x²y-ay² = -6 when z = 2.

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Q: y = x³ + 1 (x (x² 2 3 x + 3 -1 - 2x + 1)

A: The given function,      y=x3+1x3+3x2-2x-1+1

Q: Find the area of the triangle with the given vertices. (Hint: 1/2 ||u ✕ v|| is the area of the…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: dy = y cos(x), Where y(0) dx = : 1.

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Q: Evaluate the fsinz integrais belovo sin² xcsc 2x dx

A: Evaluate the integral