[1 2 31 If A = 4 5 6 l7 Q1: 8 o] Find the inverse of A by using Cayley-Hamilton theorem.

Q: 3. Consider f (x, y) = a +6V-10. Compute the following: (a) (b)

A: Given,          fx,y=x4+6y-10

Q: 1. Express the followings in the form of x + iy where r, y E R.(choose one.) (a) 금+ 부 (b) ( + ) ( –…

A: Rationalise  all the term and calculate to get the final answer.   Actually as per the barteleby…

Q: Let T: RP → R be defined by T() = Aã where -2 3 11 A = 1 -2 1 -1 -3 4 and let 6 %3D What is the…

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Q: 1 6. If at-27a? +1=0 and x+ x3 a. Prove that, a2 - V29a +1 0 34V5 b. Find the value of a- a6 c.…

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Q: Given that Z2a = 1.38 %3D Find the value of a O 0.0419 0.1676 O 0.0838

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Q: Q1: Prové by induction nzZ! ☆ (1- 1 htI ( Here JJ (Pi") stande for froduct) means (I- I

A: A detailed solution is given below.

Q: cle below, suppose m JIL =274° and mLIJK=111°. Find the follo J K (a) (b)

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Q: 4 Find the inverse of the following cubic using the substitution x=z- 3z f(x) =x + 4x 3. .....…

A: Substitute the value of x and simplify then solve for z.

Q: Let f(2)= ¹5 and let C = {z € C : |z| = 1}, described in the positive sense. Determine the value of…

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Q: -1 g(t)dt = 17 and g(t)dt = -2, find g(t)dt . %3D -3 о -15 O 11 -19 O -13 O -11 О 15 O 13 O 19

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Q: H/ sndt = then f(8)- (A) 32 (B) 0 (C) (D) (E) 5 (F) None of the above OF OE OD OA -

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Q: If y = exp(-x²) show that -2xy and hence prove that, for n > 1, %3D y(n+1) + 2xy(") + 2ny("-1) = 0.…

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Q: B. GIVEN: BF 1 AC,DE 1 AC, AB = DC, AE= CF. 18. PROVE: AAFB =ACED. F A

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Q: (1) Find an element r E D4 such that DaH R90 = V. %3D

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Q: If f(2) = cosh (In a), then f'(7) = %3D Your answer should be rounded to the nearest whole number if…

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Q: If r(t) = (V10 – t, In(t – 1), sin(2t)) - then the domain of r is О 11, 10] (1, 0) O [1, 10) O…

A: Explanation of the answer is as follows

Q: H In OJ, GH = 9, KL = 4x + 1. Find x. R 5. 5 S. GK

A: Given: GH=9,KL=4x+1  If from a centre a perpendicular is drawn to the chord, then a chord is divided…

Q: Q53- X--) (xij-Xi - X.j+X)=Zero 13D 「に )に prove that e to

A: We need to prove the given equation.

Q: If f(z) = cosh(In z“), then f' (7) = %3D %3D Your answer should be rounded to the nearest whole…

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Q: P. Im(f(z))dz O equal to the above None of these

A: no these are not equal because

Q: f A is a 2 x 2 with det(A) = 5, then det(4A-1) = %3D 80 -) 20 16 5

A: We have to choose the correct answer from the options according to the given condition

Q: Find c1, c2, and c3 such that the rule  0∫1 f(x)dx ≈ c1f(0)+c2f(0.5)+c3f(1)  is an approximation…

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Q: dy Given a DE of dz 1-r-y using simple substitution, what must be your z? Ity Answer:

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Q: If f(x) = 3z – 2z -? tan (z), then f'(1) = %3D Select one: O a. 10.5 ОБ.11 Ос. 16 Od 15.5

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Q: Find f"() if fx) = 2e* - %3D e* In 2 Ob) 20 2e* O c) 2e O d)

A: Recall:     d(eax)dx=a.eax

Q: For f(x) = 0.2x + x? – 1.2 with æo = 6.3 and æ1 = 2.1 apply steps of the method of false position…

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Q: 印 da Ify - 2e", 5+Inx O a) 1 Ob) 5+-2e " 1. c) 1 2e" d) 1 (pO Oel In(1) - 2e +66 日 F4 F5 F6 F7 F8 F9…

A: Given  y=5+ln(x)-2ex

Q: A second solution y2 for the DE z'y" - 4ry +6y = 0, can be obtained by reduction of order with the…

A: According to quetion given Differential equation x2y"-4xy'+6y=0

Q: 4. Evaluate both sides of Green's theorem, for: F = (-x²y,xy²) where C is shown in the following…

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Q: In ADEF, DE || GH. Given that FD=28, FG=12, and GH=15, find DE. D E DE%3D H. F

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Q: HW klx) = 2x+5 ㄱ 1. Find ke-¹(x) 2. Prove by kokorklok

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Q: 2h 1+h )-2 = 1 – if h<<r Prove that ( %3D r

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Q: (1. show that a) { f} = jw Flw) c)

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Q: Express in the form x + jy Q7/ (2) In(3 – j)

A: Solution:-

Q: Given f'(t) = 0.2t – e , -5t compute f(6) – f(3). f(6)- f(3)3D Type (Туре an exact answer in terms…

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Q: Consider the following integral: +oo J(2a) = | - dzerp(-20r") / dyezp(-2ay7) = { / drerp(-2aa")}?…

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Q: If y = exp(-x²) show that = -2xy and hence prove that, for n > 1, y(n+1) + 2xy(") + 2ny(n-1) = 0.…

A: Given that : y=e-x2. Therefore,  dydx=ddxe-x2=e-x2.-2x=-2xy  , as y=e-x2. Hence proved that…

Q: dy Given a DE of dr 1-z-y using simple substitution, what must be your z? z+y Answer: ||

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Q: Let z=xln(x2+y2-e4)-3xy, x=tes, y=est. If the value of 2 when s=2 and t=1 is equal to Ae2+Be4, then…

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Q: a) Let Z = 7 – 13i, find: i) Im ) ii) (Re Z)?

A: Complex Numbers: The complex number is basically the combination of a real number and an imaginary…

Q: Find Re[z-22] f Im (2-22) i f Z=a+bi

A: I have appended the formula used in the solution part

Q: Z1 is complementary to 2; 2 is complementary Given: 2 B 3 A E to 23 Prove: BD || AE

A: Prove that BD∥AE.

Q: Let z=xln(x2+y2-e4)-161xy, x=te, y=est. If the value of 2 when s=2 and t=1 is equal to Ae2+Be“, then…

A: From the chain rule, ∂z∂t=∂z∂x×∂x∂t+∂z∂y×∂y∂t Now,…

Q: L"f(t) dt = 8, Lif(:) dt = 1. Find 9. 8. Can not determine.

A: According to the rule of additivity of definite integral:

Q: Differentiate g(N) = rN| 1- with respect to N. Assume that K and r are positive constants. g'(N) = O

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Q: (a) Compute /(2) dr, given that f(b) 3 and that | af'(a) dr b(1 + f(-b)). (b) Computei (2) dz. given…

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Q: Ex . If x is adisc. r.v, Such that :- Ex) :2 Vor Lx)= 5. find: O EL-2x -1) e var (-2x- ) O E(x)

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Q: 3 (a) Given that T= 2n12g , express I in terms of T, g and n. %3D

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Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.