iii) (f x g) xh is differentiable at t and d dt 7 {(f x g) x h} xgx h + x dt dg xh +(fx g) x dt dt

Q: Assume x and y are functions of t. Evaluate dy/dt. 12) x3+y3=9;- dx dt 13) xy + x = 12; dx dt = 4, x…

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Q: 23. Find the most general antiderivative of the functions: a) f(x) = 1 –- x³ + 5x5 – 3x7. 5 – 4.x3 +…

A: Given: 1.fx=1-x3+5x5-3x7 2.g(x)=5-4x3+3x6x6 we want to calculate the antiderivative is nothing but…

Q: If f(x) = A B C -S sec²x D tanx l+et sec 3x √1+1² 1+e' 1+e lanx -dt, then f'(x) equals tanx 1+e In…

A: The Leibniz integral rule gives a formula for differentiation of a definite integral whose limits…

Q: 2. Let f(x, y) = In(x² + y²). Show that fre + fyy = 0. %3D

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Q: 1. If f(x, y)=3x' cos y– y sin x– 2.x In y- yln x-4x²y, find ôf ôf d²ƒ _ô²ƒ

A: According to question given thatf(x,y)=3x3 cosy-y2 sinx-2x ln(y)-y ln(x)-4x2y

Q: Find the linearization of g(x) = 3 + sec (t - 1) dt at x = -1.

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Q: Find the derivatie: F (+2 %3D (-t*+*z+)た =人

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Q: Find the linearization of f(x) = 9 – dt at x = 1. 2+t

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Q: Suppose that z = f(x, y) is differentiable at the point (1024, 256) withf(1024, 256) = 2 and f,…

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Q: Find F '(x). F(x) 3 tan(t) dt %3D F '(x) = 0

A: Given that, F(x) = ∫0x3tan(t) dt We have to find F'(x).

Q: 19 If f(x) = t dt then %3D f'(x) =

A: Given that  f(x) = ∫x19t4 dt  Here we have to find f'(x) .

Q: {[{ ال 1: تحق ق من دالة التالية تحق ق معادلة لابلاس :س Z = In /x2 + y² اضف ملف ك 3. fxy ل لدالة :…

A: To find  Partial derivatives of the given functions

Q: 교꾸가고 (a, y) + (0,0) (x, y) = (0,0) f(x, y) = x2+y2 is discontinuous at (0,0).

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Q: x+2 32 dt at x = 4. 2+t 6 Find the linearization of f(x) = 3-

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Q: Find the linearization of f(x) = 3+ S" sec(t - 1)dt at .2 END x = -1

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: 3. Find the interval on which the curve of y= 2 1+3t+t² dt is concave up.

A: Second derivative is positive.

Q: Suppose f(x) = integral -7x   tcos ( 1/1+t^2) dt.  Find f'(x)

A: Given,           fx=∫-7xtcos11+t2dt

Q: If f(x) I (t° + 2t + 6) dt 0. then %3D = (x), ,f

A: The function needs to be integrated first and then to the subsequent function we will be double…

Q: 8. Find the work done by F = (x² – y,x) along C:7(t)=(2cost,2sint) 0<t<2n : a) Without Green's…

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Q: Suppose that z = xy² and x and y are differentiable func- tions of t with x =2,y = when t = -1. Then…

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Q: ư (yũ + Vũ) du =

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Q: Verify Young's Theorem In(2x + y) y2 x2 + + e(x+2y)

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Q: If f is differentiable everywhere and f(1)=f(2)=π, then ∫12 f'(t)dt=0   True or false?

A: True because,

Q: 2 2 If z = f(x, y), where x = s² - t² and y = t² s² and z is differentiable, then - Select one: True…

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Q: 4x Let F (x) = S dt. Find F" (x). %3D 2+3

A: Given: Fx=∫04xdtt2+3 we know that by fundamental theorem of calculus if gx=∫pxqxfxdx then…

Q: 6. If F(x) is defined by cx²+2x esin(t) dt F(x) = Determine F'(x).

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Q: FIND THE LINEARIZATION OF f(x) = 2+ [,* dt at z= 1. %3D 1+ Lütfen birini seçin: a. L(x) = 2x – 4 b.…

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Q: of Let f (x, y) = tanh-¹(x-y) with x=e" and y= usinh (t). Then the value of dt (u,t) =(4, In 2) is…

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Q: --—-^[e'-In(2t+1)]dt, find g''(x) . dx -2 If g (x) = (A) (В Ce*- D 4 (2x + 1)² e* - In (2x + 1) 2…

A: We have to solve integral

Q: 2. Suppose that z = f (x, y) and both x and y are functions of a single variable t such that dy t2 –…

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Q: Find dy any ay of Ay of y =f(x) = x² +x at x= 10 when ax =0.1.

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Q: 2. Let F(x) = re* %3D VE dt, find F'(x). t2+sint

A: Solution is given below:

Q: prove that xy^2/x^2+y^2 is not differentiable at 0,0 when  xy^2/x^2+y^2 if (x,y) not equal to (0,0)…

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Q: 6. If F(x) is defined by cx²+2x F(x) = esin(t) dt Determine F'(x).

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Q: 3. Find an admissible extremal for the problem of minimizing J[a] {Gi² + xi + x + à} dt with x(0) 1…

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Q: 9. Explain why dt r1/I dt 1+t2 1+t? is valid for any x > 0.

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Q: 27. Find the length of the curve Vcos 2t dt y = from x = 0 to x = "/4.

A: The given curve is We know that by Second Fundamental theorem of calculus ,if F(x) is continuous on…

Q: 3. Determine if (х — 1)2, if x 1 is differentiable at x = 1.

A: Given  hx=x-12if x≤1x-1if x&gt;1

Q: 1 Find F' (0) given that F(x) : 2 dt. = r In(t+1)

A: Explanation of the answer is as follows

Q: 1 Find F'(0) given that F(x) dt. In(t + 1) 2x

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Q: Suppose that f(0) = 1, ƒ(0.5) = 2.5, f(1) = 2, and f(0.25) = f (0.75) = a. Using trapezoidal rule…

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Q: Suppose that i f(t) dt = x2 - 2x + 1. Find f(x).

A: Consider the following equation: ∫1xftdt=x2-2x+1 fx=ddxx2-2x+1=ddxx2-2ddxx+ddx1=2x-2+0=2x-2

Q: If ƒf (x) =¸ (A) (B) Sº sec²x 1+elanx In (secx) √✓ 1+tan²x tanx 1+e sec ³x tanx 1+e 1+1² tanx…

A: Using Leibnitz integral rule.

Q: 1. Show that the function x2 – y2 2xy f(x,y) ={ x2 + y? if (x,y) # 0 if (x, y) = 0 is continuous at…

A: If for every ε&gt;0, there exists a δ&gt;0, such that if |x-a|&lt;δ, |y-a|&lt;δ, then the function…

Q: 16. If f(x) = 5, (;e* G +5) dt -x, then the inflection point(s) of y = f(x) is(ar- %3D 3 A) x = 4…

A: f(x)=∫0x14t4+5dt-13x4

Q: if f(x)=integral t^3+5t^2+6, from 0 to x. what is f''(x)=?

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Q: 1 (c) If F(x) = Jtan x V2+t* dt find F'(x).

A: The given question belonging to the calculus in which we have to find the value of the derivative of…

Q: 13. Prove that the function 2x 1 dt t F(x) is a constant on the interval (0, ∞ )

A: The student has specifically asked for the solution to Question-13. Hence, that question is solved…