inh´x + cosh²x = 1 = x²arccsch(x²) then f

Q: f(x, y) = ln (2x) In (3y) + x - y - xy - 3, then fyz (2,-) is equal to

A: Given :fx,y=ln2xln3y+x-y-xy-3

Q: EX / Show that cosh x-sinhx=1

A:

Q: Find the derivative of O2 sec 2x O 2tan 2x O-2 cot2x O 1/cos2x y=In sin 2x

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Q: (5) Evaluate the definite intergral [/³ (sec²x+3x)dx. /3

A:

Q: Find the derivative of y 16 In (In(6x)). (Use symbolic notation and fractions where needed.) dy dx…

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Q: Use the first derivatives test to find local exterma of f( x) =x3 -12x on R

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Q: az ) Use Implicit differentiation to find ax and for x2 – y2 +z? – 2z = 4 ду

A:

Q: 3-S- In(x²+x)-Inx-elnx dx In(ex+1))

A: We will be using the integral formula of log function to solve the above given integral. We can…

Q: Find the derivative of Ox²2cosx + 2xsin x O 2xcos x O x² sin x + 2xcos x O x2cosx y=x²sinx

A: We know that if f(x)=g(x)h(x) then  f'(x)=g'(x)h(x)+g(x)h'(x)

Q: 2.) Investigate the derivate of the function ƒ(2)=Imz by using definiton of derivative.

A:

Q: Show that r sin (1/x) fails to have a derivative at r = 0 and even the one-sided limits (lim,-0+ (f…

A: We will prove the given statement.

Q: Q3. Show that дхду for дудх f = x² siny – 2y³ cos2x (

A:

Q: If f(x) = x cosh æ + 3 sinh x then f'(x) =

A:

Q: Ssin(x)cos(2x)sin(3x) dx O sin(6x) sin(2x) , sin(2x)cos(4x) 24 + 8 8 sin(3x)cos(3x) , sin(2x)cos(2x)…

A: We need to evaluate integral.

Q: In(5æ) Find the derivative with respect to x of y = %3D 5x y' = | %3D

A: Find the derivative

Q: 4. Show that sinx can be approximated by x-x³/6 within 0.01 on the interval [-1,1].

A: see my solution

Q: 3. Prove that cosh (2x) = cosh²x + sinh²x %3D

A:

Q: |х — 1 x5

A: Use the method of substitution to evaluate the integral. I=∫x−1x5dx=∫x−1x52dxLet u=xdu=12xdxSo,…

Q: Prove that sinh−1(x) = In( x+Vx2 +1)

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Q: 31. Verify the formulas sinh-x = In |x + Vx² + 1| coshx = In |x +Vx² – 1| (for x > 1)

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Q: Find upper and lower bounds for

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Q: The derivative of y = 3cos(8x+6) is: 1. y' = 24 sin (8x+6) 2. y' = -24 sin (8x+6) 3. y' = -24 cos…

A:

Q: Find constants c1 and c2 such that F (x) = c1 sin 3x + c2x cos 3x is anantiderivative of f(x) = 2x…

A: Given: Fx=C1sin3x+C2cos3x and the antiderivative of F(x) is fx=2x sin3x To find the constants C1 and…

Q: Prove: cosh 3x = 4 cosh° x x-3cosh.x

A: Prove that :- cosh 3x=4cosh3 x-3cosh x

Q: nd d²x/dt² as a function of if 4 = 7x sin x.

A: Given query is to find the derivative of the the expression.

Q: roo sin(2) Compute (4) dx. fo x(x²+4)

A:

Q: Find the root between [-1,0] where f (x) = (x+2)' +2x – 5 with error epsilon=0.1 by using False…

A: There are many methods to find the roots of an equation in a given interval. One among such method…

Q: 10. Show that f (x) = { x² sin(1/x) if x + 0 if x is differentiable, but the derivative is not…

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Q: 3) Suppose 2X z = xe cos 3y, find all the first and all the second derivatives.

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Q: 4. y = √esinx + 2 5. y = 4x In 4x 6. xe = sin 5x - sin 3y

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Q: compute (x2 - 8x +20) dx on the interval (0,1)

A: To evaluate the given definite integral over the open interval (0,1)

Q: Q3 : prove that : cosh?x + sinh²x =coch2x

A: L.H.S.:=cos h2x +sin h2x=(cos hx)2 +(sin hx)2  =ex+e-x22+ex-e-x22=14(ex+e-x)2+(ex-e-x)2

Q: In(8z) Siven f(z) the derivative f'(x) is 8. %3D O 8 8x o 1 O 78z 1 8x 1/8

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Q: Solve.  ln(sqaure root of z/xy)

A: We are given logarithm expression as

Q: Find the derivative of y(x) = In (7(In(x))* ). %3D (Use symbolic notation and fractions where…

A: Topic = Derivative

Q: Evaluate the integral. S sin (7x - 10) dx ㅇ cos (7x-10) +C -cos (7x - 10) + C cos (7x - 10) + C 7…

A:

Q: 17. Show that V10x + 1 and Vx + 1 grow at the same rate_ as x→o by showing that they both grow at…

A:

Q: what is the maximum value of y=sinx, 0 less than or equal to x less than or equal to 2pie, and…

A: Given function  y = sinx on  0≤x≤2π

Q: Find the derivative dy/dx of y = cos 3x O 3 sinx О З cosx O 3 sin 3x О З сos 3x none of the above

A: We can do this by doing derivative both side.

Q: Find the derivative of f(x) = ecos² (3x+1) Of(z) 6 sin(3r+1) cos(3x + 1)ecos² (3+1) O (E) None of…

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Q: Find the linearization of ƒ(x) = sqrt(1 + x) + sin x - 0.5 at x = 0

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Q: If ƒ(x) = xn, n ≥ 1, show from the definition of the derivative that ƒ'(0) = 0.

A: Now the derivative of a function f at a point 'a' is given by,

Q: Find the derivative. 3t cos (t) dt %3D O 3x cos (x4) O &va cos (x4) O 3 cos (x4) - 3x sin (x4) O cos…

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Q: Compute the derivative of y = In ( VI-2 conh z - (z² + 2) -(2- 1)

A:

Q: Find the first derivative: In 2x f (x) 1- In 2x f(x) = In (sec x) f(x) = cos (In x) f(x) = In[cos…

A: we can answer only three subparts, or the first question and the rest can be reposted. No more than…

Q: 5, i, Evaluate the first and second derivatives of the function z=2x4+3x3+2x-5 when x = 4. ii, Find…

A: The objective of the question is evaluate area and find derivatives of given functions.

Q: If g(x) : 8 + cosh(9x) find g'(x) 8+ cosh(0)

A: Answer and explanation is given below

Q: Find critical points of ƒ(x) = x² ln(x) — 1⁄x² on the interval (0, ∞).

A: Given; fx=x2lnx-12x2 ; x∈0,∞    As we know that; The critical points of the function, y=fx can be…

Q: 3. SIX f- - dx x in x√√(inx)2-9

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.