t f ex) =J3x find the difference Quatient of f-

Q: Find F′(x).

A: Here given Use the definition of the second fundamental theorem of calculus which states

Q: Ex.5. min (may [ fi Ca) =5 x,t Arz , fz G) = - x,+ 2 ] sit. 6xit Axy S 24 Xit 2X2 fz (x) = - x,+ 2x2

A:

Q: Q3) for f(v) = sec2(3v – 1) and g(v) = tan?(3v – 1) show that %3D %3! f'(v) = g'(v).

A:

Q: M is the midpoint of AB 2x + 1 and MB AM = %3D 1 ond AM

A: Given;- M is the mid point of AB AM=2x+1 and MB=3x-2    Therefore, AM=MB 2x+1=3x-2 3x-2x=1+2 x=3

Q: Q/ find the dy when y = (x+z)= リ=(メ+2)mx, %3D 2x Qul Fird dy すく e y= ノ

A: Answer

Q: Find F(s). F(s) = £{t(et + e5t)2}

A:

Q: Suppose that F(x) : = 7 r1) | f(1) dt, where %3D V3 + u6 du. f(t) =

A: We will use the Newton-Leibnitz theorem twice in the following solution and then evaluate at x = 2

Q: Find L[f]for each f(t). Q) f(t)=eat sin bt, where a,b are constants.

A:

Q: QO use best linear approximation to (F(Xiy) = ²³ to estimate the value of f at the point (0.0),…

A:

Q: If f(x,y)=xe/2,+37x?y3, then dx²əy³ at (1,1) is equal to

A:

Q: 12. Use the substitution x = sec 0, where 0 < 0 < T/2 or T < 0 < 3#/2, to evaluate Vx2 1 dx x*

A: We will evaluate the given integral by using substitution method as shown below

Q: What is the domain of r(t) = e'i + j+ (t + 1)~³k?

A:

Q: X >0, for continious f functHon Sft)dt = xarctanx fla)=?

A:

Q: J f(x)dx = f(x)dx =7, then J f(x)dx = If 4 and

A:

Q: Find the derivate of F(x): z con(2) V64 – t dt .

A: To find derivative of given function.

Q: Assume that w = f(s3 + t?) and f'(x) = ex. Find dw dw and at ds dw at dw

A:

Q: Ost<4, find F(s)=L{f (t)} using the defintion. e #1.) Given f (t) = 1 , t24

A:

Q: Suppose that F(x) = | f(t) dt, where %3D V4+ ut f(t) = du. Find F" (2). F"(2) =

A:

Q: Let F(t)=tetit j - 4+t² + t√Ek. Find SF(t) dt

A:

Q: Q2 Given z = xw? + cos y + wx , w= t , x = 2t2 , and y = 3t, find dt

A:

Q: f. . Prove false by creating a counterexample: 9(AUB) C P(A) U P(B)

A:

Q: Prove that : V.(V×A)=0

A:

Q: Using a suitable substitution, the integral T/4 9 (13+tan t)8 sec? t dt of

A: Given,          ∫0π4913+tant8sec2tdt

Q: On what interval is the curve y = 0, v- [ t2 dt t2 +t + 2 concave downward?

A: NOTE: Refresh your page if you can't see any equations. . to find the inflection point, first, we…

Q: ,use the linearity of L   determine L[f]. Q. f(t)=cosh bt, where b is constant

A: Given,

Q: et F = t+3 2i-fj+3t°k and G = e'i – 3f j+ e²* & %3D

A: Given are two vector functions F=t+3ti-t2j+3t3k and G=eti-3t3j+e2tk.

Q: Given that f(x, y)= 2x* +3x'y+6xy'-y. Find: i. f ii. f, iii. fx XX iv. fy v. Show that xy = f

A:

Q: Q3) for f(v) = sec2 (3v – 1) and g(v) = tan?(3v – 1) show that %3D f'(v) = g'(v).

A: Notice that  d/dx (tanx) = sec^2(x) d/dx(sec(x))= sec(x)tan(x) Please see the explanation below

Q: Given that f'(t) = 2sint + sec?t ,– t and f(0) = 4, find f(t) ドIN V V ドIN

A: Given, f'(t) = 2sint+sec2t  f(0) = 4 Formula used: Integral of sint = - cost Integral of sec2t =…

Q: Solve the diffgerential Eauation by Separating the Vaciables ex dy 2x %3D

A:

Q: Consider the function f(t) 9 sec?(t) – 9t?. Let F(t) be the antiderivative of f(t) with F(0) = 0.…

A:

Q: Q3) for f(t) = sec?(6t – 1) and g(t) = tan?(6t - 1) show that %3D f'(t) = g'(t).

A:

Q: Find the differential of f(x,y)=sqrt(x^2+y^3) at the point (3,2). df = ? Then use the differential…

A:

Q: Q3) for f(t) = sec²(6t – 1) and g(t) = tan?(6t – 1) show that %3D %3D f'(t) = g'(t). %3D

A:

Q: Use the Linear Approximation off (x, y) = ex2+Y at (0, 0) to estimate f (0.01, -0.02). Compare with…

A: By the method of linear approximation, if we are given a differentiable function f in two variables,…

Q: Find fr and fy for f(x,y) = I+y fz = /(r+y)? and fy = /(r+y)2

A:

Q: Let f (t) = 4t5 + Then f'(t) = At +, where A B C = %3D

A:

Q: Q2: y" + ay' + by f(t) Find a,b and f(t) so that Yp1 = et +t? – 1, Yp2 = e2t + t2 – 1 %3D %3D

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Q: Given that f(t)dz what is 13 f(s)ds? 11 enswar

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Q: Find f f'Lx) = ZR? +aX-S and %3D to FlO)=4.

A:

Q: Q4: Find fr, fry fyx and fyy for f (x, y) = e*/y

A:

Q: f(x, -0.0494 -0.3662 etter estimates by using Ar = 0.01 and Ay = 0.01. %3D 0.0516

A: Here we have to use difference quotients with ∆x=0.1 and ∆y=0.1 to estimate the fx(1,3) and fy(1,3)…

Q: Find when z% = xy, where x = f(t) and y = g(t) %3D

A: Given that z=xy2, x=ft and y=gt find ∂z∂t

Q: Differentiate. R(t) = (t + e)(2 - VE) %3D R'(t) =

A: Given function is Differentiating both sides with respect to x by using product rule of…

Q: Find f, for f(x, y) = | cos(r*) dt.

A:

Q: f (г, у) — In(ax + by) a, b ER af Land 1 Find Ja 2. Find and a f -and 3. Find dxðy дуда

A:

Q: Determine the order of the DE. а) y' + у %3D 5у? b) = t dy dt c) y' = y" + 5t2

A:

Q: Q5.a) Find if sec?y = x² + S t² dt Jsiny

A: P.S.: please ask one question at a time.

Q: Q3) for f(v) = sec2 (3v – 1) and g(v) = tan?(3v – 1) show that %3D f'(v) = g'(v). %3D

A: Given that  f(v)=sec^2(3v-1) g(x)=tan^2(3v-1) Show that f'(v)=g'(v)