1. Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval. f(x) = x' – 3x² +4x-1=D0 (0, 1)

Q: Prove that 1 + p'2 p4 where primes denote differentiation with respect to 's'. 1. x"2 + y"2 + z"2 %D

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Q: 2) Compute the approximate derivatives of In x I+ x2 fCx) at x-2, using three- endpoint formula…

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Q: Determine the equation of the tangent line to the graph of g(x) =| [1- sin(re')] dt at the In z…

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Q: Find the derivative of y with respect to x. y = tan (In 3x) O A. 1+(In 3x) 21 O B. x(1 + ( In 3x)) 1…

A: Given: The function y=tan-1ln3x, To determine: The derivative of y with respect to x,

Q: Given f(x) = 8x3 + In(x – 1). Estimate the value of f(2.01) using differential. %3D

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Q: (2-4t) sin(팔) V17- cos(27t) 1. Given f(x) = dt, find the equation of the line tangent to the graph…

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Q: Find the quadratic approximation of f at x = 0 f(x) = sin In (3x + 1) O A. Q(x) = 1 + 3x + 5x 9 B.…

A: The given function is: fx=sin ln3x+1 To find the quadratic approximation of f at x=0

Q: Find the equation of the tangent line to the graph of f(x) = 9 sin(x) + 4 cos(x) at x = in in the…

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Q: Use the intermediate Value Theorem to show that between x = 0 and x = 1, the function f(x) = 3 sinh…

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Q: (4) 3. Use implicit differentiation to find dy/dx of the following: x² - 5xy + y³ = 21

A: As per policy only first question is answered. Please refer to the image below

Q: Find the local linear approximation of cos x at xo = cos 61°. T/3 and use it to approximate

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Q: Use the Mean Value Theorem to show that f(r) = 2x sinh(r – 1) +2" – r has a critical number between…

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Q: Find the linear approximation of f(x) = ln x at a = 1 and use it to estimate In(1.2). L(x) = In(1.2)…

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Q: I. Find an equation of the tangent line to the graph of t cosh (f² – 1) dt tan-l † | f(x)%3D /1+ln…

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Q: Find the derivative of y with respect to x, t, or 0, as appropriate. y= In (In 5x) O A. 1 5x ОВ. 1 x…

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Q: Find the differential d3y of the function y=xsinhx.

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Q: Use the bise ction to approximate the solution of F(X)=Vx - cos X = 0 accurate to within 10 -3 on…

A: Bisection method: In order to find root of equation f(x)=0 in a,b such that f(a)f(b)<0 Bisect the…

Q: The linear approximation at x 0 to f(x) = sin(6x) is:

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Q: Given: f(x) = / (2 – 4t) sin() - dt %3D tan(2r) 17 – cos(2nt) Find the equation of the line tangent…

A: The tangent is a straight line to a curve that touches the curve at exactly one point. The point…

Q: 2. Find the derivative (dy/dx) of the following functions: h) y = 3x7 - 7x3 + 21x2 i) y = (x2 +…

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Q: . Compute the central difference approximations of O (h^4) for the first derivative of y = cos(x) +…

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Q: A 1125 m³ open-top rectangular tank with a square base x m on a side and y m deep is to be built…

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Q: OFind the derivative of the 1 +5 (a). f(z) = %3D T2-5

A: As per the guidelines we can solve only one question at a time so if you need more answers then…

Q: 1 Evaluate the improper intergal | dx (x2 + 9)° using the residue theorem.

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Q: Use the Mean Value Theorem to show that f(r) = 2x sinh(x – 1) + 2" – x %3D has a critical number…

A: Given: We can see that the function is continuous in [0, 1] and differentiable in (0, 1). So, the…

Q: 5. Find the derivatives (a-b) and the limit (c): (2) ± √( 1 cos (1²) dt) (0) ² (154) dt dx 1 r2+x…

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Q: The equation of tangent line of the function 36 x3 f(x) e7t dt 36 х at x=1 is Oy- V36 el764 (x-1)…

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Q: I. Find an equation of the tangent line to the graph of 1 t cosh (t² – 1) dt - f (x) = 1 tan-t 1+ln…

A: The given function is fx=∫1+lnx1tcosht2-1tan-1t dt.

Q: dx J x2-4x+5

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find an equation of the tangent line to the graph of f(x) = | t cosh (t² – 1) dt tan-lt 1+In (x) at…

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Q: Let h(x) = e*. f(x) and assume that f(ln 4) = -5 and f'(ln 4) = 6. Find the equation of the line…

A: We have to find equation of the line tangent to y=hx when x=ln(4)

Q: Determine the equation of the tangent line to the graph of g(x) = | [1- sin(re')] dt at the /In x…

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Q: The finite difference approximation of the first derivative in the simple implicit method used to…

A: given  ∂2u∂x2=∂u∂t to find the finite difference approximation of the first derivative in the…

Q: (4) 3. Use implicit differentiation to find dy/dx of the following: x2 – 6xy + y3 = 24

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Q: 1. Determine the equation of the tangent line to the graph of f(a) = [² pr+sin r = x = 0. cos (t² +…

A: Above equation of tangent is given.

Q: Find the derivative of the function. r(x) = In| 4x + e* | Oa. 4+4e4* 4x +e*x O b. none of these…

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Q: Find the equation of the tangent line to the graph of F(r)= 2z²+2r+1 evi dy at r 0. sech z

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Q: Express x = ln(7t), y = 9-t in the form y = f(x) by eliminating the parameter.

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Q: 1. Find the respect y = 2x5-x² 3x - 20 derivatives with to X using dy using o 12-1

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Find the slope of the tangent line to the graph of f(x) 2e'cos-1t dt at x = 1. In x = X'

A: Find the slope with the help of derivative of f(x) at x=1 .

Q: . Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (=) < 0. f (x) has a root in [0]. If we…

A: Newton-Raphson iteration scheme is given by  xn+1=xn-f(xn)f'(xn) We use this formula to estimate…

Q: 1 Evaluate the improper intergal dx (x² + 16)² using the residue theorem. 8.

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Q: Find the line tangent to f(x) = 3x + cos(8x) at the point wherex-0. %3D Oy-x+1 Oy-x+3 Oy-11x+1…

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Q: In (3x) Find the derivative of y with respect to x if y = sin (7 e') dt. %3D dy dx

A: Given y=∫0ln3xsin7etdt.We need to find dydx

Q: Find the actual error when the first derivative of f(x) = sin(2x) at *=1/8 s approximated by the…

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Q: Suppose that the tangent line to the graph of y = f(x) at x = 2 is y = 4x – 3 and that the tangent…

A: The given tangent line to the graph of y=fx at x=2 is y=4x-3 and the another given tangent line to…

Q: 10. Compute the central difference approximations of O(h^4 ) for the first derivative of y =cos(x) +…

A: Solution is below

Q: (1) Suppose that y is a function of r satisfying the equation 5x + 10y + 3.ry+ 5y + 6x 0. Use the…

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Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.