x+b if x<0 Is there a value of b that will make f(x)=. differentiable at x=0 ? Justify your answer. cos x if x20

Q: If u is a differentiable function of x, how do you find (d&gt;dx)(un) if n is an integer? If n is a…

A: u is a differentiable function of x.  We have to find ddxun

Q: 2. a) Find a formula for f-1 for the function y =f(x) = (x – 2)2 , x< 2 b) Evaluate the expression…

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Q: If cos-x y, then sin(2y) Is equal to 2r O 2/1- x2 2r VI - x? 2r1 - x? O dt atr = 0 has a The…

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Q: 1 35. Solve f - dx the following two ways: x² +9 (a) with the trigonometric substitution x = 3 tan…

A: To solve∫1x2+9

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Q: Sx + b, x < 0 cos x, x 2 0 Differentiable at x = 0? Give reasons for your answers. Q-9: Is there a…

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Q: 3. Given f(x)=2x +3x-1 find f'(x) then find the equation of the tangent line to f(x) at (-3,8).

A: We have to find the derivative of the given function then find the equation of the tangent line at…

Q: 2.x Given f (x) = +1, 2 + sin(Tx) that is defined over [1, 6] with a step (h= 1). Using the N.G.F.…

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A: If x is close to 0, then sinx ≈x. Consider the limits: limx→0sinxx=limx→0cosx1=cos0=1 Therefore,…

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Q: 2. Evaluate f(1) when f (x) = sinh x. А. О В. 1 e²+1 C. 2e e2-1 D. 2e E. None of the above

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Q: r(E) = 0, s° (;) Suppose f and f' are differentiable functions of r. Given = -1, and %3D g(x) – log…

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Q: h(x) = [(x − 3)√6x − x² + 9 sin¯¹ (x-³)] g(t)e-2t (1+e-2t)-1/2

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Q: a3 f 2- Find the third derivative for for f (x, y) = sin əx3 -2sin?cos()+2 sin) sin By'sini )+2…

A: The given function isf(x, y)=sinxy

Q: f (x) = xe-* – sin?x Newton Raphson (1st Method) @ x1 = 0.5 Newton Raphson (2nd Method)@ x1 = 0.5…

A: Newton Raphson Method:- Hence by Newton Raphson Method Root of the equation is 0.61447 (correct…

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Q: f(x) = x ° – cos(x) Solve this question by the Newton-Raphson method on the topic of solution of…

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Q: Find the derivative. Express answers with positive exponents. Simplifying is not necessary. (a) y =…

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Q: Let f and g be differentiable functions. Find a formula for d/dx  [3f(x)/2 − 5g(x)].  (Your answer…

A: Derivative of f(x) is f'(x). Derivative of g(x) is g'(x).

Q: |x? +3x +1 ax + In x+b ,x21. „r<1; Let f(x) = If function f(x) is differentiable at point x=1, then…

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Q: 9- 4x2 In solving for the antiderivative of f(x) = using trigonometric substitution, is x2…

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Q: Q3 Q3) Find g(f(x)) if you know that g(x) = sin(x? – 1), f(x) = cot(x) at x = 2 %3D

A: we have to find g(f(x))

Q: 2. Find d using implicit differentiation. Enclose final answers. dx (a) √x=y=√√√x + y = 5 (b) xsin y…

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Q: Find a particular solution y, of the following equation using the Method of Undetermined…

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Q: 1. Evaluate f(0) when f(x) = sinh x. A. 0 В. 1 e²+1 %3D С. 2e e2-1 2e E. None of the above

A: Given: f(x) = sinh x   To determine: f(0)

Q: sin 4.r if r>0 3. Suppose f(r) = {0 if r = 0. Find f'(0) using the definition of derivatives. if r<0…

A: This question is related to derivative, we will solve it using given information.

Q: m sin x + e", if x <0 Q NO 4: a) Find the values of m and n for which /(x) = {n(x - 1)² + x-2, if…

A: m=-6 n=3

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Q: What do we call the point at x = of the function f(x) = sinx? 2 A none of the given choices B…

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Q: A bar with insulated sides is initially at temperature 0°C throughout. The end x =0 is kept at 0°C…

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Q: (a). Find the derivative of f(x) = 4 sin x + x² cos x. (2 Marks) %3D (b). The position of a particle…

A: Follow the steps.

Q: Find an approximate value of F(1) given F'(x) = e-x² and F(0) = 2 Find an approximate value of G(-1)…

A: Express the mathematical equation for Linear Approximation. f(x)≈f(a)+(x-a)f'(a) Given, that…

Q: 3. A 2 cm long metal wire with thermal diffusivity ² = 4cm² s¹ is used to conduct heat in a machine…

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Q: f(x) X-Cos(X) ✓ Tol = 0.0005 ||X₁ = 1 1 + x 2 By using newton rafson find the solve...

A: We have f(x)=x-cos(x)1+x2,  x0=1 f'(x)=(1+sinx1+x2)-(x(x-cosx)(1+x2)32)  (using product rule of…

Q: 2. If you know (1 – a.0 s a s 1 * f(x) cos ax dx = 0 ,a>1 Find the value f(x)!

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Q: 9x2- e 2x Given by a function of x is equal to v1 – cos²x + 0. find the roots of equation with…

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Q: 1 Find all functions f that satisfy the equation (/ f(2) dz ) ( / Tim de -1. f(x)

A: Solve

Q: a- Find ?f if ?″(?)=sin?+cos?,f″(x)=sin⁡x+cos⁡x, ?′(0)=3,f′(0)=3, and  ?(0)=10. f(0)=10. b-…

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Q: Given the function: 3x? – cos(x) – 3 (KINDLY USE INCREMENTAL SEARCH METHOD) Determine the initial…

A: The function given is as follows: fx=3x2-cosx-3 (a) We are asked to find the initial values nearest…

Q: f'(t) -2 sin(t) + cos(2t) · 2 Find any critical numbers of the function.

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Q: Find the function f(x) described by the initial value problem. f’’(x)=7sinx, f’(pi)=-1, f(pi)=-4

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Q: dx = In[F(x)]+C• What is f(/3) if C = 0? For (x+x³) (x Tan-lx+1) 3 3 + 6 6. + + + -15

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