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H. e. d/dx tan(x) = sec2 = 1/cos2(x) = 1 + tan2(x). (a) Note that the function f is not continuous on (a, b) if and only if there exist a point x02 (a, b)such that f is not continuous at x0. 54(i) (2A)T = 2 AT(ii) (A + B)T = AT + BT(iii) (A – B)T = AT – BT(iv) (AB)T = BT ATSolution:(i) GivenConsider,Put the value of AL. Now,-Y T = YY is a skew symmetric matrix.

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Learn more about limits and continuity and other topics with BYJU’S and make learning more fun. Trigonometric functions:d/dx sin(x) = cos(x). e. H. d/dx cos(x) = -sin(x).

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L = f(a) = 0. I will help you online for any doubt / clarification. H. Solution:(i)Now, Comparing with equation (1) and (2)a22 = 4 and b21 = – 3a22 + b21 = 4 + (– 3) = 1(ii)Now, Comparing with equation (1) and (2)a11 = 2, a22 = 4, b11 = 2, b22 = 4a11 b11 + a22 b22 = 2 × 2 + 4 × 4 = 4 + 16 = 203. Find the value of x for a fantastic read the matrix productSolution:We know,is identity matrix of size 3. Loney and Hall Knight Solutions and Help from Ex- IITianCoordinates of a point in space, the distance between two points.

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Continuity and Differentiability is one of the most important topics which help students to understand the concepts like, continuity at a point, continuity on an interval, derivative of functions and many more. L. Net is to help and enable students to compete academically. 4 Page No: 5.

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Recall how continuity is defined using limits. If a matrix has 8 elements, what are the possible orders it can have? What if it has 5 elements?Solution:If a matrix is of order m × n elements, it has m n elements. 21. 5 SolutionsLet us have a look at some of the important concepts that are discussed in this chapter. The see this site of a curve at a point tells us the rate of change of the quantity at that point.

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L = R. Securing Higher Grades Costing Your Pocket? Book Your Assignment Help Tutor at The Lowest Price Now!Differentiation is all about finding rates of change of one quantity compared to another. So, A = [ai j] 3×4R1 = first row of A = [a11, a12, a13, a14]
So, order of matrix R1 = 1 × 4C2 = second column ofTherefore order of C2 = 3 × 14. Solution:GivenSolution:GivenSolution:GivenSolution:GivenSolution:GivenSolution:GivenI is identity matrix, soAlso given,
Now, we have to find A2, we getNow, we will find the matrix for 8A, we getSo,Substitute corresponding values from eqn (i) and (ii), we getAnd to satisfy the above condition of equality, the corresponding entries of the matrices should be equalHence,Therefore, the value of k is 7Solution:GivenTo show that f (A) = about his = A in f(x), we getI is identity matrix, soNow, we will find the matrix for A2, we getNow, we will find the matrix for 2A, we getSubstitute corresponding values from eqn (ii) and (iii) in eqn (i), we getSo,Hence ProvedSolution:GivenSoNow, we will find the matrix for A2, we getNow, we will find the matrix for λ A, we getBut given, A2 = λ A + μ ISubstitute corresponding values from equation (i) and (ii), we getAnd to satisfy the above condition of equality, the corresponding entries of the matrices should be equalHence, λ + 0 = 4 ⇒ λ = 4And also, 2λ + μ = 7Substituting the obtained value of λ in the above equation, we get2(4) + μ = 7 ⇒ 8 + μ = 7 ⇒ μ = – 1Therefore, the value of λ and μ are 4 and – 1 respectively39.

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Show that you can pick two numbers x1and x2as in the picture below, with the propertythat (x2, f (x2)) lies above the segment joining (x0, f (x0)) and (x1, f (x1)). H. NCERT Solutions, notes, sample paper for Class 1 to Class 12 for every one of the subjects refreshed for new scholastic meeting in PDF design. Use this fact to sketch a picture of what what thedefinitions above mean geometrically.

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