If x= f(u, v), y = g(u, v), u = D(r,s), and v=Y(r,s) are differentiable functions then prove that (***)-(***) (*) = 24,

Q: If r'(t) = (1,21,3r*) and r(0) = (0,1,2) then r(t) equals %3D (a) (1,r°,r'). (b) (1,r",r')+ (0,1,2)…

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Q: If f:X → Y is a bijective function,-3 then (f^(-1)•f)(x)=(fof^(-1) )(x), XEA

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Q: Suppose  f ( 200 , 300 ) = 1000and ∂ f ∂ x ( 200 , 300 ) = 12 and ∂ f ∂ y ( 200 , 300 ) = 10.…

A: Given, f(200,300)=1000 ∂f∂x(200,300)=12∂f∂y(200,300)=10

Q: az əz If z= f(x,y), where x = (s+1) , y = (s- t). Then Əs at

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Q: d g(s) be two differentiable functions in R and f  (2) = 8, g(2) =0, f(4) = 10 , and g(4) = 8 Then…

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Q: 36. Let f be a twice-differentiable function of z such that, when z = c, f is increasing, concave…

A: We have given function of x which is twice-differentiable such that when x=c, f is increasing,…

Q: If we have that f: R → Ris a continuous function , in which f'(7) = 6 and f(7) = -2 an equation of…

A: We have to find out tangent line

Q: (7) If f(z) is analytic function show that: (+)rox-4rt =

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Q: Prove f-1(E U F) = f-\(E) U f-1(F)

A: We have to prove that f−1E∪F=f−1E∪f−1F. Let x∈f−1E∪F hence, x∈f−1E∪F⇔fx∈E∪F…

Q: suppose that f (u, v) = ue", where u =rs and v =r + s. The composite function f(u, v) is equal to:…

A: A composite function is one which is made of other functions or in other words function values are…

Q: f(x) = 3 tan x. (a) Solve f(x) = -3. (b) For what values of x is f(x) < -3 on the interval π π…

A: (a) Let, f(x)=3tan(x) Now, f(x)=-3⇒3tanx=-3⇒tanx=-1⇒tanx=-tanπ4⇒tanx=tannπ-π4⇒x=nπ-π4where…

Q: 2. Suppose that {f(t)} = F(s) with F a differentiable function and that {f(t)} exists. Then L{-te*…

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Q: If f is a function from X to Y and C, D are subsets of Y then A O f(C-D) =f(C)-f (D) B f'(Cn…

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Q: (6) . that Let f(x) be a differentiable function on the interval (0, 0) such f (x*) = 3f(x), for…

A: We have to prove the given equation.

Q: If f. g and h are differentiable functions at a, then f(g+h) is differentiable at a and ( f(g+…

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Q: If f is a differentiable function at a, then xf is differentiable at a and (af)'(a) is: Select one:…

A: We need to evaluate the following expression xf'a

Q: 4. Let f(x, y)=2x*y' . Find f,(x,y)

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Q: {(u)= (u² -3)*

A: Given the function is  f(u) = 12u2-32. We have to find f'(u).

Q: 4. If /(r.y)=- , find f, and f,. V+y

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Q: Let f be a differentiable function of one variable, and let w = f(p), where p = (x² + y² + z?)!/2.…

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Q: 12. Let f(z,y) = < then f(1,2) = (b) 글 (d) 금

A: Given :fx, y=x-yx+y-1

Q: Let F(x , y , z) = g(y) + h(z) + 5 In(x - 2) , where g(y) and h(z) are differentiable functions of…

A: If a function is a function of more than one independent variable then the derivative of this…

Q: 2. At what points of R² is the function continuous? (sin(x² + y²) x² + y² f(x, y) = 0, -, if (x, y)…

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Q: For questions 8-10, let f(x) be a function defined everywhere such that f"(x) = 3x² – 12x. What are…

A: Definition used -                   Point of inflection - A point where the concavity of graph of…

Q: 7. Find : y = (x* = 5«)a0n 5x, (b). y = x2

A: We can find the derivative as below

Q: Assume that f: R→ R and g: R → R are infinitely differentiable functions. Prove the following…

A: We have given that ,  are both infinitely differentiable.We need to prove that , We will use…

Q: If f', and y are continuous on [a, b] and derivable on Ja, b[, then show that there is a value c…

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Q: Suppose that f is a twice differentiable function (everywhere). such that f(5) = 3 and f'(5) = 7 and…

A: Given data f( 5 ) = 3 f'( 5 ) = 7 f''( 5 ) = 1

Q: Let f(z) = r? – 9z + 5 with domain 0 <r < 4, 5. Calculate (f ')(-3). Note: Round to two decimal…

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Q: Let f(x) and g(s) be two differentiable functions in R and f (2) = 8, g(2) =0, f(4) = 10, and g(4) =…

A: Solution :-